Paul Manuel | Kuwait University (original) (raw)
Uploads
Papers by Paul Manuel
arXiv (Cornell University), Jan 20, 2021
Applied Mathematics and Computation, Dec 1, 2018
The Computer Journal, Jan 12, 2016
International journal of mathematics and soft computing, Jul 21, 2012
arXiv (Cornell University), Jul 14, 2019
International journal of pure and applied mathematics, 2017
A set S of vertices in a graph G is said to be a perfect k-dominating set if every vertex in V −S... more A set S of vertices in a graph G is said to be a perfect k-dominating set if every vertex in V −S is adjacent to exactly k vertices of S. The perfect k-domination number, γkp(G) is the minimum cardinality of a perfect k-dominating set of G. In this paper, we construct a minimum perfect k-dominating set where k = 1, 2, 3, 4 for infinite diamond lattice. AMS Subject Classification: 05C69
International Journal of Computer Mathematics: Computer Systems Theory, 2021
Graph is a mathematical model represented by points and lines joining certain pairs of points. Th... more Graph is a mathematical model represented by points and lines joining certain pairs of points. These points are addressed as vertices or nodes and the lines are addressed as edges or links. Graph embedding is a mapping of guest graph G into host graph H satisfying certain conditions. Embedding has been studied for many networks in the literature. The Recursive Circulant has several attractive topological properties. Though the embedding of parallel architectures such as Hypercubes and Mesh into Recursive Circulant has been studied, the embedding of Recursive Circulant into other architectures has not been taken up so far. In this paper, we compute the wirelength of embedding even into paths (MinLA), 1-rooted complete binary trees, regular caterpillars and ladders.
Lecture Notes in Computer Science, 2015
arXiv (Cornell University), Oct 23, 2022
Cogent Mathematics, 2016
The aim of this paper was to generate nanotopological structure on the power set of vertices of s... more The aim of this paper was to generate nanotopological structure on the power set of vertices of simple digraphs using new definition neighbourhood of vertices on out linked of digraphs. Based on the neighbourhood we define the approximations of the subgraphs of a graph. A new nanotopological graph reduction to symbolic circuit analysis is developed in this paper. By means of structural equivalence on nanotopology induced by graph we have framed an algorithm for detecting patent infringement suit.
The Computer Journal, 2016
Electronic Government, an International Journal
Parallel Processing Letters, 2015
Graph embedding is an important technique that maps a logical graph into a host graph, usually an... more Graph embedding is an important technique that maps a logical graph into a host graph, usually an interconnection network. In this paper, we compute the exact wirelength of embedding Christmas trees into trees. Moreover, we present an algorithm for embedding Christmas trees into caterpillars with dilation 3 proving that the lower bound obtained in [30] is sharp. Further, we solve the maximum subgraph problem for Christmas trees and provide a linear time algorithm to compute the exact wirelength of embedding Christmas trees into trees.
The Computer Journal, 2015
Graph embedding problems have gained importance in the field of interconnection networks for para... more Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. In this paper, we introduce a technique to obtain a lower bound for dilation of an embedding. Moreover, we give algorithms to compute exact dilation of embedding circulant network into a triangular grid, Tower of Hanoi graph and Sierpinski gasket graph, proving that the lower bound obtained is sharp.
Bulletin of the Australian Mathematical Society, 2018
The paper introduces a graph theory variation of the general position problem: given a graph GGG,... more The paper introduces a graph theory variation of the general position problem: given a graph GGG, determine a largest set SSS of vertices of GGG such that no three vertices of SSS lie on a common geodesic. Such a set is a max-gp-set of GGG and its size is the gp-number textgp(G)\text{gp}(G)textgp(G) of GGG. Upper bounds on textgp(G)\text{gp}(G)textgp(G) in terms of different isometric covers are given and used to determine the gp-number of several classes of graphs. Connections between general position sets and packings are investigated and used to give lower bounds on the gp-number. It is also proved that the general position problem is NP-complete.
Australasian Journal of Combinatorics
Open Mathematics, 2017
Geodesic covering problems form a widely researched topic in graph theory. One such problem is ge... more Geodesic covering problems form a widely researched topic in graph theory. One such problem is geodetic problem introduced by Harary et al. [Math. Comput. Modelling, 1993, 17, 89-95]. Here we introduce a variation of the geodetic problem and call it strong edge geodetic problem. We illustrate how this problem is evolved from social transport networks. It is shown that the strong edge geodetic problem is NP-complete. We derive lower and upper bounds for the strong edge geodetic number and demonstrate that these bounds are sharp. We produce exact solutions for trees, block graphs, silicate networks and glued binary trees without randomization.
The Computer Journal, 2016
International Journal of Applied Mathematics and Computer Science
ABSTRACT
arXiv (Cornell University), Jan 20, 2021
Applied Mathematics and Computation, Dec 1, 2018
The Computer Journal, Jan 12, 2016
International journal of mathematics and soft computing, Jul 21, 2012
arXiv (Cornell University), Jul 14, 2019
International journal of pure and applied mathematics, 2017
A set S of vertices in a graph G is said to be a perfect k-dominating set if every vertex in V −S... more A set S of vertices in a graph G is said to be a perfect k-dominating set if every vertex in V −S is adjacent to exactly k vertices of S. The perfect k-domination number, γkp(G) is the minimum cardinality of a perfect k-dominating set of G. In this paper, we construct a minimum perfect k-dominating set where k = 1, 2, 3, 4 for infinite diamond lattice. AMS Subject Classification: 05C69
International Journal of Computer Mathematics: Computer Systems Theory, 2021
Graph is a mathematical model represented by points and lines joining certain pairs of points. Th... more Graph is a mathematical model represented by points and lines joining certain pairs of points. These points are addressed as vertices or nodes and the lines are addressed as edges or links. Graph embedding is a mapping of guest graph G into host graph H satisfying certain conditions. Embedding has been studied for many networks in the literature. The Recursive Circulant has several attractive topological properties. Though the embedding of parallel architectures such as Hypercubes and Mesh into Recursive Circulant has been studied, the embedding of Recursive Circulant into other architectures has not been taken up so far. In this paper, we compute the wirelength of embedding even into paths (MinLA), 1-rooted complete binary trees, regular caterpillars and ladders.
Lecture Notes in Computer Science, 2015
arXiv (Cornell University), Oct 23, 2022
Cogent Mathematics, 2016
The aim of this paper was to generate nanotopological structure on the power set of vertices of s... more The aim of this paper was to generate nanotopological structure on the power set of vertices of simple digraphs using new definition neighbourhood of vertices on out linked of digraphs. Based on the neighbourhood we define the approximations of the subgraphs of a graph. A new nanotopological graph reduction to symbolic circuit analysis is developed in this paper. By means of structural equivalence on nanotopology induced by graph we have framed an algorithm for detecting patent infringement suit.
The Computer Journal, 2016
Electronic Government, an International Journal
Parallel Processing Letters, 2015
Graph embedding is an important technique that maps a logical graph into a host graph, usually an... more Graph embedding is an important technique that maps a logical graph into a host graph, usually an interconnection network. In this paper, we compute the exact wirelength of embedding Christmas trees into trees. Moreover, we present an algorithm for embedding Christmas trees into caterpillars with dilation 3 proving that the lower bound obtained in [30] is sharp. Further, we solve the maximum subgraph problem for Christmas trees and provide a linear time algorithm to compute the exact wirelength of embedding Christmas trees into trees.
The Computer Journal, 2015
Graph embedding problems have gained importance in the field of interconnection networks for para... more Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. In this paper, we introduce a technique to obtain a lower bound for dilation of an embedding. Moreover, we give algorithms to compute exact dilation of embedding circulant network into a triangular grid, Tower of Hanoi graph and Sierpinski gasket graph, proving that the lower bound obtained is sharp.
Bulletin of the Australian Mathematical Society, 2018
The paper introduces a graph theory variation of the general position problem: given a graph GGG,... more The paper introduces a graph theory variation of the general position problem: given a graph GGG, determine a largest set SSS of vertices of GGG such that no three vertices of SSS lie on a common geodesic. Such a set is a max-gp-set of GGG and its size is the gp-number textgp(G)\text{gp}(G)textgp(G) of GGG. Upper bounds on textgp(G)\text{gp}(G)textgp(G) in terms of different isometric covers are given and used to determine the gp-number of several classes of graphs. Connections between general position sets and packings are investigated and used to give lower bounds on the gp-number. It is also proved that the general position problem is NP-complete.
Australasian Journal of Combinatorics
Open Mathematics, 2017
Geodesic covering problems form a widely researched topic in graph theory. One such problem is ge... more Geodesic covering problems form a widely researched topic in graph theory. One such problem is geodetic problem introduced by Harary et al. [Math. Comput. Modelling, 1993, 17, 89-95]. Here we introduce a variation of the geodetic problem and call it strong edge geodetic problem. We illustrate how this problem is evolved from social transport networks. It is shown that the strong edge geodetic problem is NP-complete. We derive lower and upper bounds for the strong edge geodetic number and demonstrate that these bounds are sharp. We produce exact solutions for trees, block graphs, silicate networks and glued binary trees without randomization.
The Computer Journal, 2016
International Journal of Applied Mathematics and Computer Science
ABSTRACT
Covering problems belong to the foundation of graph theory. There are several types of covering p... more Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination problem), covering the vertex set by cliques (clique covering problem), covering the vertex set by independent sets (coloring problem), and covering the vertex set by paths or cycles. A similar concept which is partitioning problem is also equally important. Lately research in graph theory has produced unprecedented growth because of its various application in engineering and science. The covering and partitioning problem by paths itself have produced a sizable volume of literatures. The research on these problems is expanding in multiple directions and the volume of research papers is exploding. It is the time to simplify and unify the literature on different types of the covering and partitioning problems. The problems considered in this article are path cover problem, induced path cover problem, isometric path cover problem, path partition problem, induced path partition problem and isometric path partition problem. The objective of this article is to summarize the recent developments on these problems, classify their literatures and correlate the inter-relationship among the related concepts.
The classical no-three-in-line problem is to find the maximum number of points that can be placed... more The classical no-three-in-line problem is to find the maximum number of points that can be placed in the n×n grid so that no three points lie on a line. Given a set S of points in an Euclidean plane, the General Position Subset Selection Problem is to find a maximum subset S of S such that no three points of S are collinear. Motivated by these problems, the following graph theory variation is introduced: Given a graph G, determine a largest set S of vertices of G such that no three vertices of S lie on a common geodesic. Such a set is a gp-set of G and its size is the gp-number gp(G) of G. Upper bounds on gp(G) in terms of different isometric covers are given and used to determine the gp-number of several classes of graphs. Connections between general position sets and packings are investigated and used to give lower bounds on the gp-number. It is also proved that the general position problem is NP-complete.
Geodesic covering problems form a widely researched topic in graph theory. One such problem is ge... more Geodesic covering problems form a widely researched topic in graph theory. One such problem is geodetic problem introduced by Harary et al. [18]. Here we introduce a variation of the geodetic problem and call it strong edge geode-tic problem. We illustrate how this problem is evolved from social transport networks. It is shown that the strong edge geodetic problem is NP-complete. We derive lower bounds for the strong edge geodetic number and demonstrate that these bounds are sharp and non-trivial. We produce exact solutions for trees, block graphs, silicate networks and glued binary trees without random-ization.