[PDF] Top 20 Strong Perfect Domination in Graphs

... the domination number of ...a perfect dominating set of G if |N (v) ∩ S| = 1 for each v ∊ V- ...trivial perfect dominating set consisting of all vertices in ...the perfect dominating set of G ... See full document

... is strong. A subset D of V is called a strong vertex dominating set of G (𝜎, 𝜇) if for every 𝑣 ∈ 𝑉 − 𝐷, there exists 𝑢 ∈ 𝐷 such that u dominates ...A strong vertex dominating set D is called a ... 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

... 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

... independent domination number of a graph is the minimum cardinality of an independent dominating set (Haynes et ...a strong split dominating set if the induced subgraph is totally disconnected with at least ... 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

... DℎF 3G FF, B -*/ 5 C 5 DℎF 3G H . In this paper we will find the values of perfect domination number for Bishops, Kings and Rooks graphs on a × chessboard. In section 3 we show the placement of ... See full document

... Proof: Let G be a Γ-perfect graph and suppose that G contains a critical graph H(A, B) as a semi-induced subgraph. We have β(H) < k, where k = |A| = |B|. Consider in the graph G the induced subgraph F = hA ∪ ... 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 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

... : is a complete fuzzy graph with two nodes i.e., a strong arc with its nodes. By above theorem, both the vertices of : is in the 2-dominating set of G. Thus the fuzzy graph G has all the 2 nodes in the ... See full document

... minimal strong ev weight m dominating set exists, the above result does not exist, since the complement of a strong ev weight m dominating set will not be a strong ev weight m dominating ...minimal ... 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

... Suppose that G has a perfect matching M. Then every vertex of G is M-saturated. Therefore every vertex of S is M-saturated. Since S is independent, every line of M has either one end in S and other end in V−S or ... 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

... 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

... of domination in graphs introduced by Claude Berge in 1958 and Oystein Ore in 1962 [6] is currently receiving much ...the domination in graphs became an area of study by many ...of ... See full document

... Γ-perfect graphs in terms of some family of forbidden induced subgraphs, and show that the class of Γ-perfect graphs is a subclass of IR-perfect ...absorbantly perfect ... See full document