[PDF] Top 20 Strong line domination in graphs

... the Line graph of a graph is a graph whose set of vertices is the union of the set of edges of in which two vertices are adjacent if and only if the corresponding edges of are ...a strong Line ... See full document

... K and isolated vertices. Since G is a disconnected graph and    G  1 , G has at least three vertices. Assume that G has m induced sub-graphs K 2 . For solving the problem it is enough to show that m  2 . On ... See full document

... of domination in graph was initiated by Berge ...valued graphs. The domination in vertices and edges of an S-valued graph has been studied in (Jeyalakshmi et ...mixed domination on S- valued ... 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

... discussed domination in fuzzy graphs. They defined domination using effective edges in fuzzy ...discussed domination in fuzzy graph using strong ...discussed domination, ... 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

... 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 cardinal, strong and equivalent products of path ...connected domination number of Cartesian product of path will be reported in the subsequent ... See full document

... a strong edge dominating set if for every edge e  E (G) - S, there is an edge f  S with deg f ≥ deg e, and e is adjacent to ...The strong edge domination number is denoted by 𝛾′ 𝑠 ...edge ... See full document

... minus domination number of Jahangir graphs and find a result for the minus domination number of the line graph of any general sunlet ...minus domination number after adding an edge to ... 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 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

... 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

... Proof.let be a maximum independent set of vertices in and  ∀ ∈ 〈 〉 is isolates. Then ( − ) ∪ is a strong split dominating set of . Since for each vertex ∈ ( − ) ∪ either is an isolated vertex in < ( − ) ∪ > ... See full document

... Let G be a graph. A set D ⊆ V (G ) is said to be a strong point set dominating set (spsd-set) of G. if for each set S ⊆ V − D , there exists a vertex u ∈ D such that the sub graph S U { } u induced by S U { } u ... See full document

... complement line domination number for some standard graphs like Cycle, Path, Complete bipartite, Wheel, Banana, Crown graph, Comb tree, Helm graph, 𝐾 𝑛 + graph, 𝐾 𝑚 ,𝑛 + graph, Book graph, Friendship ... See full document

... Definition 2.8. Let G and H be two graphs on n and m ver- tices, k and l edges, respectively. The edge corona G♦H of G and H is defined as the graph obtained by taking one copy of G and k copies of H, and then ... See full document

... Kulli and Janakiram introduced the concept of strong non-split domination number of a graph [10]. Throughout this paper D=(V,A) is a finite directed graph with neither loops nor multiple arcs(but pairs of ... See full document

... the domination number of G and is denoted by    G ...total domination number of G , denoted by  t   G is the minimum cardinality of total dominating set of G ... 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