Laszlo Liptak - Academia.edu (original) (raw)

Papers by Laszlo Liptak

Research paper thumbnail of On the Extraconnectivity of Arrangement Graphs

Research paper thumbnail of Conditional fractional matching preclusion for burnt pancake graphs and pancake-like graphs

International Journal of Computer Mathematics: Computer Systems Theory, Sep 7, 2022

Research paper thumbnail of 4-ORDERED Hamiltonicity for Some Chordal Ring Graphs

Journal of Interconnection Networks, Sep 1, 2010

A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G... more A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G containing these k vertices in the specified order. It is k-ordered Hamiltonian if, in addition, the required cycle is Hamiltonian. The question of the existence of an infinite class of 3-regular 4-ordered Hamiltonian graphs was posed in 1997 by Ng and Schultz.13 At the time, the only known examples were K4 and K3,3. Some progress was made in 2008 by Mészáros,12 when the Peterson graph was found to be 4-ordered and the Heawood graph was proved to be 4-ordered Hamiltonian; moreover, an infinite class of 3-regular 4-ordered graphs was found. In 2010 a subclass of generalized Petersen graphs was shown to be 4-ordered by Hsu et al.,10 with an infinite subset of this subclass being 4-ordered Hamiltonian, thus answering the open question. In this paper we find another infinite class of 3-regular 4-ordered Hamiltonian graphs, part of a subclass of the chordal ring graphs. In addition, we classify precisely which of these graphs are 4-ordered Hamiltonian.

Research paper thumbnail of Conditional Fractional Matching Preclusion for Burnt Pancake Graphs and Pancake-Like Graphs (Extended Abstract)

Lecture Notes in Computer Science, 2021

Research paper thumbnail of Facets with fixed defect of the stable set polytope

Mathematical Programming, Jun 1, 2000

The stable set polytope of a graph is the convex hull of the 0-1 vectors corresponding to stable ... more The stable set polytope of a graph is the convex hull of the 0-1 vectors corresponding to stable sets of vertices. To any nontrivial facet n i=1 a i x i ≤ b of this polytope we associate an integer δ, called the defect of the facet, by δ = n i=1 a i − 2b. We show that for any fixed δ there is a finite collection of graphs (called "basis") such that any graph with a facet of defect δ contains a subgraph which can be obtained from one of the graphs in the basis by a simple subdivision operation.

Research paper thumbnail of The stable set problem and the lift-and-project ranks of graphs

Mathematical Programming, Sep 1, 2003

Research paper thumbnail of Fault Resiliency of Cayley Graphs Generated by Transpositions

International Journal of Foundations of Computer Science, Oct 1, 2007

The star graph Sn, proposed by [1], has many advantages over the n-cube. It is shown in [2] that ... more The star graph Sn, proposed by [1], has many advantages over the n-cube. It is shown in [2] that when a large number of vertices are deleted from Sn, the resulting graph can have at most two components, one of which is small. In this paper, we show that Cayley graphs generated by transpositions have this property.

Research paper thumbnail of Matching preclusion and conditional matching preclusion for regular interconnection networks

Discrete Applied Mathematics, Sep 1, 2012

The matching preclusion number of a graph is the minimum number of edges whose deletion results i... more The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices and neither perfect matchings nor almost-perfect matchings. In this paper, we prove general results regarding the matching preclusion number and the conditional matching preclusion number as well as the classification of their respective optimal sets for regular graphs. We then use these general results to study the problems for Cayley graphs generated by 2-trees and the hyper Petersen networks.

Research paper thumbnail of Matching preclusion for some interconnection networks

Networks, 2007

ABSTRACT The matching preclusion number of a graph is the minimum number of edges whose deletion ... more ABSTRACT The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. In this paper, we find this number for various classes of interconnection networks and classify all the optimal solutions. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(2), 173–180 2007

Research paper thumbnail of Linearly many faults in 2-tree-generated networks

Networks, 2009

In this article we consider a class of Cayley graphs that are generated by certain 3-cycles on th... more In this article we consider a class of Cayley graphs that are generated by certain 3-cycles on the alternating group A n. These graphs are generalizations of the alternating group graph AG n. We look at the case when the 3-cycles form a "tree-like structure," and analyze its fault resiliency. We present a number of structural theorems and prove that even with linearly many vertices deleted, the remaining graph has a large connected component containing almost all vertices.

Research paper thumbnail of A complete classification of which <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(n,k)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span></span></span></span>-star graphs are Cayley graphs

arXiv (Cornell University), Mar 17, 2017

The (n, k)-star graphs are an important class of interconnection networks that generalize star gr... more The (n, k)-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al. (Graphs and Combinatorics 2017) and complete the classification of all the (n, k)-star graphs that are Cayley.

Research paper thumbnail of A conjecture on determining which <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(n,k)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span></span></span></span>-star graphs are not Cayley graphs

arXiv (Cornell University), Mar 17, 2017

The (n, k)-star graphs are an important class of interconnection networks that generalize star gr... more The (n, k)-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al. (Graphs and Combinatorics 2017) and complete the classification of all the (n, k)-star graphs that are Cayley.

Research paper thumbnail of On the Conditional Diagnosability of Cayley Graphs Generated by 2-trees and Related Networks

In this note, we utilize existing results to derive the exact value of the conditional diagnosabi... more In this note, we utilize existing results to derive the exact value of the conditional diagnosability for Cayley graphs generated by 2-trees, which generalize the alternating group graphs. In addition, the corresponding problem for arrangement graphs and hyper Petersen networks will also be discussed.

Research paper thumbnail of Generalized Matching Preclusion in Bipartite Graphs

Theory and applications of graphs, 2018

The matching preclusion number of a graph with an even number of vertices is the minimum number o... more The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal such sets are precisely sets of edges incident to a single vertex, whose deletion creates an isolated vertex, which is an obstruction to the existence of a perfect matching. The conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond these, and it is defined as the minimum number of edges whose deletion results in a graph with neither isolated vertices nor perfect matchings. In this paper we generalize this concept to get a hierarchy of stronger matching preclusion properties in bipartite graphs, and completely characterize such properties of complete bipartite graphs and hypercubes.

Research paper thumbnail of Structure and Substructure Connectivity of Hypercube-Like Networks

Parallel Processing Letters, Sep 1, 2020

The connectivity of a graph [Formula: see text], [Formula: see text], is the minimum number of ve... more The connectivity of a graph [Formula: see text], [Formula: see text], is the minimum number of vertices whose removal disconnects [Formula: see text], and the value of [Formula: see text] can be determined using Menger’s theorem. It has long been one of the most important factors that characterize both graph reliability and fault tolerability. Two extensions to the classic notion of connectivity were introduced recently: structure connectivity and substructure connectivity. Let [Formula: see text] be isomorphic to any connected subgraph of [Formula: see text]. The [Formula: see text]-structure connectivity of [Formula: see text], denoted by [Formula: see text], is the cardinality of a minimum set [Formula: see text] of connected subgraphs in [Formula: see text] such that every element of [Formula: see text] is isomorphic to [Formula: see text], and the removal of [Formula: see text] disconnects [Formula: see text]. The [Formula: see text]-substructure connectivity of [Formula: see text], denoted by [Formula: see text], is the cardinality of a minimum set [Formula: see text] of connected subgraphs in [Formula: see text] whose removal disconnects [Formula: see text] and every element of [Formula: see text] is isomorphic to a connected subgraph of [Formula: see text]. The family of hypercube-like networks includes many well-defined network architectures, such as hypercubes, crossed cubes, twisted cubes, and so on. In this paper, both the structure and substructure connectivity of hypercube-like networks are studied with respect to the [Formula: see text]-star [Formula: see text] structure, [Formula: see text], and the [Formula: see text]-cycle [Formula: see text] structure. Moreover, we consider the relationships between these parameters and other concepts.

Research paper thumbnail of A Unified Approach to the Conditional Diagnosability of Interconnection Networks

Journal of Interconnection Networks, Sep 1, 2012

The conditional diagnosability of interconnection networks has been studied in a number of ad-hoc... more The conditional diagnosability of interconnection networks has been studied in a number of ad-hoc methods resulting in various conditional diagnosability results. In this paper, we utilize these existing results to give an unified approach in studying this problem. Following this approach, we derive the exact value of the conditional diagnosability for a number of interconnection networks including Cayley graphs generated by 2-trees (which generalize alternating group graphs), arrangement graphs (which generalize star graphs and alternating group graphs), hyper Petersen networks, and dual-cube like networks (which generalize dual-cubes.)

Research paper thumbnail of Diagnosability of Cayley graphs generated by transposition trees with missing edges

Information Sciences, Jul 1, 2013

Recently, strong local diagnosability properties for star graphs were proved even with missing ed... more Recently, strong local diagnosability properties for star graphs were proved even with missing edges. We extend these results to Cayley graphs generated by transposition trees.

Research paper thumbnail of Orienting Cayley graphs generated by transposition trees

Computers & mathematics with applications, Jun 1, 2008

Day and Tripathi [K. Day, A. Tripathi, Unidirectional star graphs, Inform. Process. Lett. 45 (199... more Day and Tripathi [K. Day, A. Tripathi, Unidirectional star graphs, Inform. Process. Lett. 45 (1993) 123-129] proposed an assignment of directions on the star graphs and derived attractive properties for the resulting directed graphs. Cheng and Lipman [E.

Research paper thumbnail of Matching preclusion and conditional matching preclusion problems for tori and related Cartesian products

Discrete Applied Mathematics, Aug 1, 2012

The matching preclusion number of a graph with an even number of vertices is the minimum number o... more The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. It is natural to look for obstruction sets beyond those induced by a single vertex. The conditional matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph with no isolated vertices that has no perfect matchings. In this companion paper of Cheng et al. (Networks (NET 1554)), we find these numbers for a number of popular interconnection networks including hypercubes, star graphs, Cayley graphs generated by transposition trees and hyper-stars.

Research paper thumbnail of On the G-Extra Connectivity of Augmented Cubes

Social Science Research Network, 2023

Research paper thumbnail of On the Extraconnectivity of Arrangement Graphs

Research paper thumbnail of Conditional fractional matching preclusion for burnt pancake graphs and pancake-like graphs

International Journal of Computer Mathematics: Computer Systems Theory, Sep 7, 2022

Research paper thumbnail of 4-ORDERED Hamiltonicity for Some Chordal Ring Graphs

Journal of Interconnection Networks, Sep 1, 2010

A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G... more A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G containing these k vertices in the specified order. It is k-ordered Hamiltonian if, in addition, the required cycle is Hamiltonian. The question of the existence of an infinite class of 3-regular 4-ordered Hamiltonian graphs was posed in 1997 by Ng and Schultz.13 At the time, the only known examples were K4 and K3,3. Some progress was made in 2008 by Mészáros,12 when the Peterson graph was found to be 4-ordered and the Heawood graph was proved to be 4-ordered Hamiltonian; moreover, an infinite class of 3-regular 4-ordered graphs was found. In 2010 a subclass of generalized Petersen graphs was shown to be 4-ordered by Hsu et al.,10 with an infinite subset of this subclass being 4-ordered Hamiltonian, thus answering the open question. In this paper we find another infinite class of 3-regular 4-ordered Hamiltonian graphs, part of a subclass of the chordal ring graphs. In addition, we classify precisely which of these graphs are 4-ordered Hamiltonian.

Research paper thumbnail of Conditional Fractional Matching Preclusion for Burnt Pancake Graphs and Pancake-Like Graphs (Extended Abstract)

Lecture Notes in Computer Science, 2021

Research paper thumbnail of Facets with fixed defect of the stable set polytope

Mathematical Programming, Jun 1, 2000

The stable set polytope of a graph is the convex hull of the 0-1 vectors corresponding to stable ... more The stable set polytope of a graph is the convex hull of the 0-1 vectors corresponding to stable sets of vertices. To any nontrivial facet n i=1 a i x i ≤ b of this polytope we associate an integer δ, called the defect of the facet, by δ = n i=1 a i − 2b. We show that for any fixed δ there is a finite collection of graphs (called "basis") such that any graph with a facet of defect δ contains a subgraph which can be obtained from one of the graphs in the basis by a simple subdivision operation.

Research paper thumbnail of The stable set problem and the lift-and-project ranks of graphs

Mathematical Programming, Sep 1, 2003

Research paper thumbnail of Fault Resiliency of Cayley Graphs Generated by Transpositions

International Journal of Foundations of Computer Science, Oct 1, 2007

The star graph Sn, proposed by [1], has many advantages over the n-cube. It is shown in [2] that ... more The star graph Sn, proposed by [1], has many advantages over the n-cube. It is shown in [2] that when a large number of vertices are deleted from Sn, the resulting graph can have at most two components, one of which is small. In this paper, we show that Cayley graphs generated by transpositions have this property.

Research paper thumbnail of Matching preclusion and conditional matching preclusion for regular interconnection networks

Discrete Applied Mathematics, Sep 1, 2012

The matching preclusion number of a graph is the minimum number of edges whose deletion results i... more The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices and neither perfect matchings nor almost-perfect matchings. In this paper, we prove general results regarding the matching preclusion number and the conditional matching preclusion number as well as the classification of their respective optimal sets for regular graphs. We then use these general results to study the problems for Cayley graphs generated by 2-trees and the hyper Petersen networks.

Research paper thumbnail of Matching preclusion for some interconnection networks

Networks, 2007

ABSTRACT The matching preclusion number of a graph is the minimum number of edges whose deletion ... more ABSTRACT The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. In this paper, we find this number for various classes of interconnection networks and classify all the optimal solutions. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(2), 173–180 2007

Research paper thumbnail of Linearly many faults in 2-tree-generated networks

Networks, 2009

In this article we consider a class of Cayley graphs that are generated by certain 3-cycles on th... more In this article we consider a class of Cayley graphs that are generated by certain 3-cycles on the alternating group A n. These graphs are generalizations of the alternating group graph AG n. We look at the case when the 3-cycles form a "tree-like structure," and analyze its fault resiliency. We present a number of structural theorems and prove that even with linearly many vertices deleted, the remaining graph has a large connected component containing almost all vertices.

Research paper thumbnail of A complete classification of which <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(n,k)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span></span></span></span>-star graphs are Cayley graphs

arXiv (Cornell University), Mar 17, 2017

The (n, k)-star graphs are an important class of interconnection networks that generalize star gr... more The (n, k)-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al. (Graphs and Combinatorics 2017) and complete the classification of all the (n, k)-star graphs that are Cayley.

Research paper thumbnail of A conjecture on determining which <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(n,k)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span></span></span></span>-star graphs are not Cayley graphs

arXiv (Cornell University), Mar 17, 2017

The (n, k)-star graphs are an important class of interconnection networks that generalize star gr... more The (n, k)-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al. (Graphs and Combinatorics 2017) and complete the classification of all the (n, k)-star graphs that are Cayley.

Research paper thumbnail of On the Conditional Diagnosability of Cayley Graphs Generated by 2-trees and Related Networks

In this note, we utilize existing results to derive the exact value of the conditional diagnosabi... more In this note, we utilize existing results to derive the exact value of the conditional diagnosability for Cayley graphs generated by 2-trees, which generalize the alternating group graphs. In addition, the corresponding problem for arrangement graphs and hyper Petersen networks will also be discussed.

Research paper thumbnail of Generalized Matching Preclusion in Bipartite Graphs

Theory and applications of graphs, 2018

The matching preclusion number of a graph with an even number of vertices is the minimum number o... more The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal such sets are precisely sets of edges incident to a single vertex, whose deletion creates an isolated vertex, which is an obstruction to the existence of a perfect matching. The conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond these, and it is defined as the minimum number of edges whose deletion results in a graph with neither isolated vertices nor perfect matchings. In this paper we generalize this concept to get a hierarchy of stronger matching preclusion properties in bipartite graphs, and completely characterize such properties of complete bipartite graphs and hypercubes.

Research paper thumbnail of Structure and Substructure Connectivity of Hypercube-Like Networks

Parallel Processing Letters, Sep 1, 2020

The connectivity of a graph [Formula: see text], [Formula: see text], is the minimum number of ve... more The connectivity of a graph [Formula: see text], [Formula: see text], is the minimum number of vertices whose removal disconnects [Formula: see text], and the value of [Formula: see text] can be determined using Menger’s theorem. It has long been one of the most important factors that characterize both graph reliability and fault tolerability. Two extensions to the classic notion of connectivity were introduced recently: structure connectivity and substructure connectivity. Let [Formula: see text] be isomorphic to any connected subgraph of [Formula: see text]. The [Formula: see text]-structure connectivity of [Formula: see text], denoted by [Formula: see text], is the cardinality of a minimum set [Formula: see text] of connected subgraphs in [Formula: see text] such that every element of [Formula: see text] is isomorphic to [Formula: see text], and the removal of [Formula: see text] disconnects [Formula: see text]. The [Formula: see text]-substructure connectivity of [Formula: see text], denoted by [Formula: see text], is the cardinality of a minimum set [Formula: see text] of connected subgraphs in [Formula: see text] whose removal disconnects [Formula: see text] and every element of [Formula: see text] is isomorphic to a connected subgraph of [Formula: see text]. The family of hypercube-like networks includes many well-defined network architectures, such as hypercubes, crossed cubes, twisted cubes, and so on. In this paper, both the structure and substructure connectivity of hypercube-like networks are studied with respect to the [Formula: see text]-star [Formula: see text] structure, [Formula: see text], and the [Formula: see text]-cycle [Formula: see text] structure. Moreover, we consider the relationships between these parameters and other concepts.

Research paper thumbnail of A Unified Approach to the Conditional Diagnosability of Interconnection Networks

Journal of Interconnection Networks, Sep 1, 2012

The conditional diagnosability of interconnection networks has been studied in a number of ad-hoc... more The conditional diagnosability of interconnection networks has been studied in a number of ad-hoc methods resulting in various conditional diagnosability results. In this paper, we utilize these existing results to give an unified approach in studying this problem. Following this approach, we derive the exact value of the conditional diagnosability for a number of interconnection networks including Cayley graphs generated by 2-trees (which generalize alternating group graphs), arrangement graphs (which generalize star graphs and alternating group graphs), hyper Petersen networks, and dual-cube like networks (which generalize dual-cubes.)

Research paper thumbnail of Diagnosability of Cayley graphs generated by transposition trees with missing edges

Information Sciences, Jul 1, 2013

Recently, strong local diagnosability properties for star graphs were proved even with missing ed... more Recently, strong local diagnosability properties for star graphs were proved even with missing edges. We extend these results to Cayley graphs generated by transposition trees.

Research paper thumbnail of Orienting Cayley graphs generated by transposition trees

Computers & mathematics with applications, Jun 1, 2008

Day and Tripathi [K. Day, A. Tripathi, Unidirectional star graphs, Inform. Process. Lett. 45 (199... more Day and Tripathi [K. Day, A. Tripathi, Unidirectional star graphs, Inform. Process. Lett. 45 (1993) 123-129] proposed an assignment of directions on the star graphs and derived attractive properties for the resulting directed graphs. Cheng and Lipman [E.

Research paper thumbnail of Matching preclusion and conditional matching preclusion problems for tori and related Cartesian products

Discrete Applied Mathematics, Aug 1, 2012

The matching preclusion number of a graph with an even number of vertices is the minimum number o... more The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. It is natural to look for obstruction sets beyond those induced by a single vertex. The conditional matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph with no isolated vertices that has no perfect matchings. In this companion paper of Cheng et al. (Networks (NET 1554)), we find these numbers for a number of popular interconnection networks including hypercubes, star graphs, Cayley graphs generated by transposition trees and hyper-stars.

Research paper thumbnail of On the G-Extra Connectivity of Augmented Cubes

Social Science Research Network, 2023