Ali Sahal | University of Mysore (original) (raw)
Papers by Ali Sahal
In this paper, we obtain structural properties and eccentricity properties of G<sup>+−.<... more In this paper, we obtain structural properties and eccentricity properties of G<sup>+−.</sup> We establish characterization of graphs whose G<sup>+−</sup> are Eulerian. In addition, we obtain middle graphs, total graphs and quasi-total graphs of <em>G</em>, which are isomorphic to G<sup>+−</sup>.
International Journal of Computer Applications, 2014
By a graph G = (V,E) we mean a finite, undirected graph with neither loops nor multiple edges. Th... more By a graph G = (V,E) we mean a finite, undirected graph with neither loops nor multiple edges. The order and size of G are denoted by n and m, respectively. For graph theoretic terminology we refer to Chartrand and Lesnaik [2].
Abstract. Let G = (V1, V2, E) be a bipartite graph. Then G is called cocom-plete bipartite graph,... more Abstract. Let G = (V1, V2, E) be a bipartite graph. Then G is called cocom-plete bipartite graph, if for any two vertices u, v ∈ Vi, i = 1, 2 there exists P3 containing them. In this paper, we introduce the concepts of Weak and Strong cocomplete bipartite graphs. We study some properties of these graphs. We also develop furthers results on cocomplete bipartite graph. 1.
MATCH Communications in Mathematical and in Computer Chemistry
A co-complete bipartite graph is a bipartite graph G = (V1, V2, E) such that for any two vertices... more A co-complete bipartite graph is a bipartite graph G = (V1, V2, E) such that for any two vertices u, v ∈ Vi, i = 1, 2, there exists P3 containing them. A co-complete k-partite graph G = (V1, V2,..., Vk, E), k ≥ 2 is a graph with smallest number k of disjoint parts in which any pair of vertices in the same part are at distance two. The number of parts in co-complete k-partite graph G is denoted by k(G). In this paper, we initiate a study of this class in graphs and we obtain a characterization for such graphs. Each set in the partition has subpartitions such that each set in the subparti-tion induces K1 or any two vertices in this subpartition are joined byP3 and this result has significance in providing a stable network.
Abstract: Let G = (V,E) be a graph, D ⊆ V and u be any vertex in D. Then the out degree of u with... more Abstract: Let G = (V,E) be a graph, D ⊆ V and u be any vertex in D. Then the out degree of u with respect to D denoted by odD (u), is defined as odD (u) = |N(u) ∩ (V −D)|. A subset D ⊆ V (G) is called a near equitable dominating set of G if for every v ∈ V −D there exists a vertex u ∈ D such that u is adjacent to v and |od
MATCH Communications in Mathematical and in Computer Chemistry
Let G be a graph. A total hub set S of G is a subset of V (G) such that every pair of vertices (w... more Let G be a graph. A total hub set S of G is a subset of V (G) such that every pair of vertices (whether adjacent or nonadjacent) of V − S are connected by a path, whose all intermediate vertices are in S. The total hub number ht(G) is then defined to be the minimum cardinality of a total hub set of G. In this paper, the total hub number for several classes of graphs is computed, bounds in terms of other graph parameters are also determined.
International Journal of Mathematical Archive Issn 2229 5046, Apr 29, 2014
L et be a graph, let and be any vertex in . Then the out degree of with respect to denoted by , ... more L et be a graph, let and be any vertex in . Then the out degree of with respect to denoted by , is defined as . A subset is called a near equitable dominating set of if for every there exists a vertex such that is adjacent to and . A near equitable dominating set is called a strong total near equitable dominating set (stned-set) if for every vertex there exists such that is adjacent to and . The minimum cardinality of stned-set of is called the strong total near equitable domination number of and is denoted by . In this paper, we initiate a study of this parameter.
Asian Journal of Mathematics and Applications, Apr 25, 2013
Let G = (V1, V2,E) be a bipartite graph. Then G is called cocomplete bipartite graph, if for any ... more Let G = (V1, V2,E) be a bipartite graph. Then G is called cocomplete bipartite graph, if for any two vertices u, v \in Vi, i = 1, 2 there exists P3 containing them. In this paper, we introduce the concepts of Weak and Strong cocomplete bipartite graphs. We study some properties of these graphs. We also develop furthers results on cocomplete bipartite graph.
Proceedings of the Jangjeon Mathematical Society, 2012
ABSTRACT Let G=(V 1 ,V 2 ,E) be a bipartite graph. Then G is called cocomplete bipartite graph, i... more ABSTRACT Let G=(V 1 ,V 2 ,E) be a bipartite graph. Then G is called cocomplete bipartite graph, if for any two vertices u,v∈V i , i=1,2, there exists P 3 containing them. In this paper, we study some properties of cocomplete bipartite graphs. We obtain the necessary and sufficient condition for a cocomplete bipartite graph to be complete bipartite. We also study the condition under which a bipartite graph becomes cocomplete bipartite graph. Further, we establish the relation between balanced bipartite graph and cocomplete bipartite graph. We find the bound for the number of edges of cocomplete bipartite graph.
Let G = (V;E) be a graph, D ⊆ V and u be any vertex in D. Then the out degree of u with respect t... more Let G = (V;E) be a graph, D ⊆ V and u be any vertex in D. Then the out degree of u with respect to D denoted by odD(u), is dened as odD(u) = |N(u) ∩ (V − D)|. A subset D ⊆ V (G) is called a near equitable dominating set of G if for every v ∈ V − D there exists a vertex u ∈ D such that u is adjacent to v and |odD(u) − odV D(v)| 6 1. A near equitable dominating set D is said to be a connected near equitable dominating set if the subgraph ⟨D⟩ induced by D is connected. The minimum of the cardinality of a connected near equitable dominating set of G is called the connected near equitable domination number and is denoted by cne(G). In this paper results involving this parameter are found, bounds for cne(G) are obtained. Connected near equitable domatic partition in a graph G is studied.
Transactions on Combinatorics, 2013
An equitable domination has interesting application in the context of social networks. In a netwo... more An equitable domination has interesting application in the context of social networks. In a network, nodes with nearly equal capacity may interact with each other in a better way. In the society persons with nearly equal status, tend to be friendly. In this paper, we introduce new variant of equitable domination of a graph. Basic properties and some interesting results have been obtained.
Let G = (V,E) be a graph, DV and u be any vertex in D. Then the out degree of u with respect to D... more Let G = (V,E) be a graph, DV and u be any vertex in D. Then the out degree of u with respect to D denoted by odD(u), is defined as odD(u) = |N(u) \ (V D)|. A subset DV (G) is called a near equitable dominating set of G if for every v 2 V D there exists a vertex u 2 D such that u is adjacent to v and |odD(u) odV −D(v)| � 1. A near equitable dominating set D is said to be a total near equitable dominating set (tned-set) if every vertex w 2 V is adjacent to an element of D. The minimum cardinality of tned-set of G is called the total near equitable domination number of G and is denoted by tne(G). The maximum order of a partition of V into tned-sets is called the total near equitable domatic number of G and is denoted by dtne(G). In this paper we initiate a study of these
An equitable domination has interesting application in the context of social networks. In a netwo... more An equitable domination has interesting application in the context of social networks. In a network, nodes with nearly equal capacity may interact with each other in a better way. In the society persons with nearly equal status, tend to be friendly. In this paper, we introduce new variant of equitable domination of a graph. Basic properties and some interesting results have been obtained. G is called the domination number (upper domination number) of G and is denoted by γ(G) (Γ(G)). An excellent treatment of the fundamentals of domination is given in the book by Haynes et al. [4]. A survey of several advanced topics in domination is given in the book edited by Haynes et al. [5]. Various types of domination have been defined and studied by several authors and more than 75 models of domination are listed in the appendix of Haynes et al. [4]. A double star is the tree obtained from two disjoint stars K 1,n and K 1,m by connecting their centers.
A co-complete k -partite graph G = (V1,V2, … ,Vk, E), k ≥ 2 is a graph with the smallest number k... more A co-complete k -partite graph G = (V1,V2, … ,Vk, E), k ≥ 2 is a graph with the smallest number k of disjoint parts in which any pair of vertices in the same part is at a distance two. The number of parts in co-complete k -partite graph G is denoted by k (G). In this paper, we investigate k() , k(L(G)), k(M(G)) and k(T(G)), where , L(G) , M(G) and T(G) are complement graph, line graph, middle graph and total graph, respectively of some standard graphs. We also discuss the relationship between them. Each set in the partition has subpartitions such that each set in the subpartition induces K1 or any two vertices in this subpartition are at distance two and this result has significance in providing a stable network.
The vertex neighbor integrity of a connected graph G = (V;E) is denoted as V NI(G) and defined by... more The vertex neighbor integrity of a connected graph G = (V;E) is denoted as V NI(G) and defined by where S is any vertex subversion strategy of G and m(G=S) is the number of vertices in the largest component of G=S. In this paper we obtain vertex neighbor integrity of middle graph of some standard graphs and combinations of these graphs.
An equitable domination has interesting application in the context of social networks. In a netwo... more An equitable domination has interesting application in the context of social networks. In a network, nodes with nearly equal capacity may interact with each other in a better way. In the society persons with nearly equal status, tend to be friendly. In this paper, we introduce new variant of equitable domination of a graph. Basic properties and some interesting results have been obtained.
let V D ⊆ and u be any vertex in D . Then the out degree of u with respect to D denoted by ) (u o... more let V D ⊆ and u be any vertex in D . Then the out degree of u with respect to D denoted by ) (u od ) (G stne γ . In this paper, we initiate a study of this parameter. Mathematics Subject Classification: 05C.
In this paper, we obtain structural properties and eccentricity properties of G<sup>+−.<... more In this paper, we obtain structural properties and eccentricity properties of G<sup>+−.</sup> We establish characterization of graphs whose G<sup>+−</sup> are Eulerian. In addition, we obtain middle graphs, total graphs and quasi-total graphs of <em>G</em>, which are isomorphic to G<sup>+−</sup>.
International Journal of Computer Applications, 2014
By a graph G = (V,E) we mean a finite, undirected graph with neither loops nor multiple edges. Th... more By a graph G = (V,E) we mean a finite, undirected graph with neither loops nor multiple edges. The order and size of G are denoted by n and m, respectively. For graph theoretic terminology we refer to Chartrand and Lesnaik [2].
Abstract. Let G = (V1, V2, E) be a bipartite graph. Then G is called cocom-plete bipartite graph,... more Abstract. Let G = (V1, V2, E) be a bipartite graph. Then G is called cocom-plete bipartite graph, if for any two vertices u, v ∈ Vi, i = 1, 2 there exists P3 containing them. In this paper, we introduce the concepts of Weak and Strong cocomplete bipartite graphs. We study some properties of these graphs. We also develop furthers results on cocomplete bipartite graph. 1.
MATCH Communications in Mathematical and in Computer Chemistry
A co-complete bipartite graph is a bipartite graph G = (V1, V2, E) such that for any two vertices... more A co-complete bipartite graph is a bipartite graph G = (V1, V2, E) such that for any two vertices u, v ∈ Vi, i = 1, 2, there exists P3 containing them. A co-complete k-partite graph G = (V1, V2,..., Vk, E), k ≥ 2 is a graph with smallest number k of disjoint parts in which any pair of vertices in the same part are at distance two. The number of parts in co-complete k-partite graph G is denoted by k(G). In this paper, we initiate a study of this class in graphs and we obtain a characterization for such graphs. Each set in the partition has subpartitions such that each set in the subparti-tion induces K1 or any two vertices in this subpartition are joined byP3 and this result has significance in providing a stable network.
Abstract: Let G = (V,E) be a graph, D ⊆ V and u be any vertex in D. Then the out degree of u with... more Abstract: Let G = (V,E) be a graph, D ⊆ V and u be any vertex in D. Then the out degree of u with respect to D denoted by odD (u), is defined as odD (u) = |N(u) ∩ (V −D)|. A subset D ⊆ V (G) is called a near equitable dominating set of G if for every v ∈ V −D there exists a vertex u ∈ D such that u is adjacent to v and |od
MATCH Communications in Mathematical and in Computer Chemistry
Let G be a graph. A total hub set S of G is a subset of V (G) such that every pair of vertices (w... more Let G be a graph. A total hub set S of G is a subset of V (G) such that every pair of vertices (whether adjacent or nonadjacent) of V − S are connected by a path, whose all intermediate vertices are in S. The total hub number ht(G) is then defined to be the minimum cardinality of a total hub set of G. In this paper, the total hub number for several classes of graphs is computed, bounds in terms of other graph parameters are also determined.
International Journal of Mathematical Archive Issn 2229 5046, Apr 29, 2014
L et be a graph, let and be any vertex in . Then the out degree of with respect to denoted by , ... more L et be a graph, let and be any vertex in . Then the out degree of with respect to denoted by , is defined as . A subset is called a near equitable dominating set of if for every there exists a vertex such that is adjacent to and . A near equitable dominating set is called a strong total near equitable dominating set (stned-set) if for every vertex there exists such that is adjacent to and . The minimum cardinality of stned-set of is called the strong total near equitable domination number of and is denoted by . In this paper, we initiate a study of this parameter.
Asian Journal of Mathematics and Applications, Apr 25, 2013
Let G = (V1, V2,E) be a bipartite graph. Then G is called cocomplete bipartite graph, if for any ... more Let G = (V1, V2,E) be a bipartite graph. Then G is called cocomplete bipartite graph, if for any two vertices u, v \in Vi, i = 1, 2 there exists P3 containing them. In this paper, we introduce the concepts of Weak and Strong cocomplete bipartite graphs. We study some properties of these graphs. We also develop furthers results on cocomplete bipartite graph.
Proceedings of the Jangjeon Mathematical Society, 2012
ABSTRACT Let G=(V 1 ,V 2 ,E) be a bipartite graph. Then G is called cocomplete bipartite graph, i... more ABSTRACT Let G=(V 1 ,V 2 ,E) be a bipartite graph. Then G is called cocomplete bipartite graph, if for any two vertices u,v∈V i , i=1,2, there exists P 3 containing them. In this paper, we study some properties of cocomplete bipartite graphs. We obtain the necessary and sufficient condition for a cocomplete bipartite graph to be complete bipartite. We also study the condition under which a bipartite graph becomes cocomplete bipartite graph. Further, we establish the relation between balanced bipartite graph and cocomplete bipartite graph. We find the bound for the number of edges of cocomplete bipartite graph.
Let G = (V;E) be a graph, D ⊆ V and u be any vertex in D. Then the out degree of u with respect t... more Let G = (V;E) be a graph, D ⊆ V and u be any vertex in D. Then the out degree of u with respect to D denoted by odD(u), is dened as odD(u) = |N(u) ∩ (V − D)|. A subset D ⊆ V (G) is called a near equitable dominating set of G if for every v ∈ V − D there exists a vertex u ∈ D such that u is adjacent to v and |odD(u) − odV D(v)| 6 1. A near equitable dominating set D is said to be a connected near equitable dominating set if the subgraph ⟨D⟩ induced by D is connected. The minimum of the cardinality of a connected near equitable dominating set of G is called the connected near equitable domination number and is denoted by cne(G). In this paper results involving this parameter are found, bounds for cne(G) are obtained. Connected near equitable domatic partition in a graph G is studied.
Transactions on Combinatorics, 2013
An equitable domination has interesting application in the context of social networks. In a netwo... more An equitable domination has interesting application in the context of social networks. In a network, nodes with nearly equal capacity may interact with each other in a better way. In the society persons with nearly equal status, tend to be friendly. In this paper, we introduce new variant of equitable domination of a graph. Basic properties and some interesting results have been obtained.
Let G = (V,E) be a graph, DV and u be any vertex in D. Then the out degree of u with respect to D... more Let G = (V,E) be a graph, DV and u be any vertex in D. Then the out degree of u with respect to D denoted by odD(u), is defined as odD(u) = |N(u) \ (V D)|. A subset DV (G) is called a near equitable dominating set of G if for every v 2 V D there exists a vertex u 2 D such that u is adjacent to v and |odD(u) odV −D(v)| � 1. A near equitable dominating set D is said to be a total near equitable dominating set (tned-set) if every vertex w 2 V is adjacent to an element of D. The minimum cardinality of tned-set of G is called the total near equitable domination number of G and is denoted by tne(G). The maximum order of a partition of V into tned-sets is called the total near equitable domatic number of G and is denoted by dtne(G). In this paper we initiate a study of these
An equitable domination has interesting application in the context of social networks. In a netwo... more An equitable domination has interesting application in the context of social networks. In a network, nodes with nearly equal capacity may interact with each other in a better way. In the society persons with nearly equal status, tend to be friendly. In this paper, we introduce new variant of equitable domination of a graph. Basic properties and some interesting results have been obtained. G is called the domination number (upper domination number) of G and is denoted by γ(G) (Γ(G)). An excellent treatment of the fundamentals of domination is given in the book by Haynes et al. [4]. A survey of several advanced topics in domination is given in the book edited by Haynes et al. [5]. Various types of domination have been defined and studied by several authors and more than 75 models of domination are listed in the appendix of Haynes et al. [4]. A double star is the tree obtained from two disjoint stars K 1,n and K 1,m by connecting their centers.
A co-complete k -partite graph G = (V1,V2, … ,Vk, E), k ≥ 2 is a graph with the smallest number k... more A co-complete k -partite graph G = (V1,V2, … ,Vk, E), k ≥ 2 is a graph with the smallest number k of disjoint parts in which any pair of vertices in the same part is at a distance two. The number of parts in co-complete k -partite graph G is denoted by k (G). In this paper, we investigate k() , k(L(G)), k(M(G)) and k(T(G)), where , L(G) , M(G) and T(G) are complement graph, line graph, middle graph and total graph, respectively of some standard graphs. We also discuss the relationship between them. Each set in the partition has subpartitions such that each set in the subpartition induces K1 or any two vertices in this subpartition are at distance two and this result has significance in providing a stable network.
The vertex neighbor integrity of a connected graph G = (V;E) is denoted as V NI(G) and defined by... more The vertex neighbor integrity of a connected graph G = (V;E) is denoted as V NI(G) and defined by where S is any vertex subversion strategy of G and m(G=S) is the number of vertices in the largest component of G=S. In this paper we obtain vertex neighbor integrity of middle graph of some standard graphs and combinations of these graphs.
An equitable domination has interesting application in the context of social networks. In a netwo... more An equitable domination has interesting application in the context of social networks. In a network, nodes with nearly equal capacity may interact with each other in a better way. In the society persons with nearly equal status, tend to be friendly. In this paper, we introduce new variant of equitable domination of a graph. Basic properties and some interesting results have been obtained.
let V D ⊆ and u be any vertex in D . Then the out degree of u with respect to D denoted by ) (u o... more let V D ⊆ and u be any vertex in D . Then the out degree of u with respect to D denoted by ) (u od ) (G stne γ . In this paper, we initiate a study of this parameter. Mathematics Subject Classification: 05C.