[PDF] Top 20 Secure Edge Domination in Graphs

... The domination number γ(G) of G is the minimum cardinality of a dominating set of ...many domination parameters are given in the books by Kulli in [2, 3, ...an edge dominating set if every ... See full document

... The edge domination was introduced by Arumugam and Velammal ...The edge domination problem has many applications in resource allocation, network routing and encoding theory problems [1, ...of ... See full document

... minimal edge dominating set since for any edge e i ∈ F , F − { } e i is not an edge dominating set for N ( e i ) in G ...an edge of G can dominate at most n ( n − 1 ) + 1 distinct edges ... See full document

... In this section, we introduce the notion of strong and weak edge - vertex mixed domination in S valued graph and prove some simple results. In paper (Kiruthiga Deepa, 2017), we have defined the terms ev ... See full document

... . Edge dominating sets were studied by ...an edge dominating set of G if every edge in E – F is adjacent to at least one edge in ...an edge dominating set of G if every edge e ∈ ... See full document

... An edge dominating set X of is called a connected edge dominating set of G if the induced subgraph X is ...connected edge domination number  c    G (or  c  for short ) of G is the ... See full document

... each edge a set of colors chosen from the power set of {1,2} ...each edge E(G) such that g( we have ⋃ = {1,2},then g is called 2-Rainbow edge domination function(2REDF) and the weight w(g) of ... See full document

... in graphs. Mitchell and Hedetniemi [7] and Xu [14] have worked on edge domination ...2-tuple domination problem on trapezoid ...total domination related parameters and in [1, 13] have ... See full document

... minimum secure dominating set of G. If V – D contains a secure dominating set D' of G, then D' is called an inverse secure dominating set with respect to ...inverse secure domination ... See full document

... an edge dominating set of G if every edge not in F is adjacent to some edge in ...The edge domination number (G) of G is the minimum cardinality taken over all edge dominating ... See full document

... We begin with simple, finite, connected and undirected graph G with vertex set V (G) and edge set E(G). The set S ⊆ V (G) of vertices in a graph G is called a dominating set if every vertex v ∈ V (G) is either an ... See full document

... Let G be a finite, simple, undirected graph on n vertices with vertex set V(G) and edge set E(G). For graph theoretic terminology refer to Harary [5], Buckley and Harary [3]. Definition 1.1. The open ... See full document

... Let 𝑉 and 𝐸 represent vertex set and edge set respectively for graph 𝐺. Consider a vertex 𝑣 belongs to 𝑉, the number of edges incident on a vertex 𝑣 is called the degree of it and is denoted by 𝑑𝑒𝑔(𝑣) with minimum ... See full document

... bipartite graphs with equal edge domination number and maximum matching cardinality are characterized by Dutton and Klostermeyer [9] while Yannakakis and Gavril [17] have shown that edge ... See full document

... Now, assume that    G  3 . In this case, we show that there exists at most an edge between the vertices V   G  N   v . On the contrary we assume that there exist at least two edges between the vertices of ... See full document

... Domination in graph theory is studied by Cockayne, Hedetneimi and Dawes [1, 3]. Jasintha Quadras et al. initiated the quest of finding the total bondage number and total domination number of windmill graph, ... See full document

... an edge dominating set of G if every edge in is adjacent to at least one edge in ...an edge dominating set of G if for every edge , there exists an edge such that and have a ... See full document

... A secure fuzzy edge dominating set of a fuzzy graph G is a fuzzy edge dominating set F⊆E with the property that for each edge e∈E – F, there exists f∈F adjacent to e such that (F – {f}) ∪ {e} ... See full document

... M  x x  x . Since B is an edge dominating set of G ,   M is independent. Furthermore, since G is connected and   M is independent, each vertex x i in M is adjacent to some z j  z j  u j or v k  in G . Let ... See full document

... valued graphs, where S is a semiring. In graph theory, domination of graphs is the most powerful area of research for, it has several applications in other areas of ...vertex domination on S− ... See full document