[PDF] Top 20 Strong Efficient Domination In Graphs

... Throughout this paper, we consider finite, undirected, simple graphs. Let G = (V,E) be a graph. The degree of any vertex u in G is the number of edges incident with u and is denoted by deg u. The minimum and ... See full document

... a strong total dominating set of ...all strong neighbors are fuzzy end nodes. Since K is a strong total dominating set of there exists some node in K which dominates ...the strong neighbor of ... See full document

... connected graphs of order n with Strong Roman domination numbers 2 n  2 , 2 n  3 , 2 n  4 and 2 n  5 ...with Strong Roman domination number 2 n  6 ... See full document

... In (Kiruthiga Deepa, 2016) we have defined the terms ev weight m dominating set, in which we have considered the weight of edges which dominates the weight of the vertices belonging to the spanning sub graph of N S (e). ... See full document

... Proof. Let 𝐷 = {𝑢 1 , 𝑢 2 , … . . 𝑢 𝑛 } be a minimum strong vertex dominating set of G. Arrange the elements of D such that 𝑑 𝑠 (𝑢 𝑖 ) ≤ 𝑑 𝑠 (𝑢 𝑖+1 ). Since D is minimal, 𝑑 𝑠 (𝑢 𝑖 ) ≠ 0 for 1 ≤ 𝑖 ≤ 𝑛. Also, since ... See full document

... strong neighbourhood of the node # is defined as $ % (#) = { ∈ : (#, ) is a strong arc}. A subset D of V is called a dominating set of a fuzzy graph G if for every ∈ V− D, there exist # ∈ D such that # ... See full document

... of graphs G and H is the graph with vertex set V(G) V(H) × and edge set is ( , )( , ) u a v b ∈ E G H ( × ) if and only if uv ∈ E G ( ) and ab ∈ E H ( ) ...two graphs G and H is the graph G ⋈ H with ... See full document

... The domination number𝛾(G) of G is the minimum cardinality of the dominating set of ...of domination in graphs and its advanced topics are given in ...defined strong(weak) domination in ... See full document

... connected domination number of the product of path graphs as cardinal, strong and equivalent ...connected domination number and is denoted by ߛ rtc ...the domination numbers of ܲ ௠ ܲ ௡ ... See full document

... a strong Line dominating set if every vertex in 〈 〉 is strongly dominated by at least one vertex in .... Strong Line domination number of is the minimum cardinality of strong Line dominating ... See full document

... a strong nonsplit block dominating set if the induced subgraph〈 [ ( )] − 〉 is ...The strong nonsplit block domination number ( ) of is the minimum cardinality of strong nonsplit block ... See full document

... the strong geodetic problem. Here the domination concept is combined with strong geodetic concept resulting in Strong geodetic domination of graphs and few results are ... See full document

... By a graph, it is meant that a finite, undirected graph without loops and multiple edges. Let G be a graph with vertex V and edge set E. Let p = |V (G)| and q = |E (G)|. The minimum and maximum degrees of vertices in G ... See full document

... simple graphs are considered. The concept of domination in graphs was introduced by ...on domination have been published by ...an efficient dominating set of G if for every vertex u ∈ ... See full document

... We consider simple, finite, connected and undirected graph G with vertex set V (G) and edge set E (G). For all stan- dard terminology and notations we follow West [20] while the terms related to the theory of ... See full document

... of strong non-split domination in directed graph D has been introduced by considering the dominating set S is a strong non-split dominating set if the complement of S is complete A dominating set S ... See full document

... the strong line set dominating number of G and is denote by ϑ sl ' ( G ) ...paper Strong Line set Dominating set are analyse with respect to the strong domination parameter for separable ... See full document

... the domination number of 𝐺 and denoted by 𝛾(𝐺) ...of domination number of a graph appeared was in ...on domination in graphs like (7, 8, 9, ...hn- domination number are stated. Also, ... See full document

... N [X] = N (X) ∪ X. Denote by δ = δ(G) and ∆ = ∆(G) the minimum and maximum degrees of vertices of G, respectively. The following well-known definitions can be found in [13]. A set X is called a dominating set if every ... See full document

... The domination in graphs is one of the concepts in graph theory which has attracted many researchers to work on ...of domination models are available in existing literature - Independent ... See full document