[PDF] Top 20 Complementary Perfect Domination Number of Regular Graphs

... 2 regular graphs with X icp and 3 regular graphs with X icp and describe an upper limit for number of vertices in d-regular ...d-regular graphs with X icp (G ) and ... See full document

... This placement will cover the entire chessboard with each cell being dominated exactly once and gives minimum number of Bishops required to satisfy the condition of perfect domination number ... See full document

... independence number, the upper domination number and the upper irredundance number, ...Γ- perfect if β(H) = Γ(H), for every induced subgraph H of ...Γ-perfect graphs in ... See full document

... regular graphs. One of the current interests of researchers is Butterfly graphs, because they are studied as a topology of parallel machine ... See full document

... non-split domination in ...non-split domination number of G is the minimum cardinality of a non-split dominating ...introduced complementary tree domination number of a graph and ... See full document

... Proof: Let E 0 be the maximum set of l-edges in G such that β(G 0 ) < k, where V (G 0 ) = V (G) and E(G 0 ) = E(G) − E 0 . Since E 0 is maximum and deleting all l-edges from G produces the graph with independence ... See full document

... independent domination was formalized by Berge [4] and Ore [14] in ...independent domination number and the notation i(G) were introduced by Cockayne and Hedetniemi in [5, ...in regular ... See full document

... of domination in graphs was introduced by ...the domination number of G and is denoted by ...in graphs was introduced by ...maximum number of classes of a domatic partition of G ... See full document

... The domination number γ(G) of G is the minimum cardinality of a dominating ...two complementary tree dominating set,if for each u ∈ V – D, d(u,v) ≤ 2 for some v in D and also <V – D> is a ... See full document

... A fuzzy set, introduced by Zadeh[8], gives the degree of membership of an object in a given set. Zhang [9] initiated the concept of a bipolar fuzzy set as a generalization of a fuzzy set. A bipolar fuzzy set is an ... See full document

... strong complementary acyclic dominating set if S is a strong dominating set and the induced subgraph V - S is ...strong complementary acyclic dominating set of G is called the strong complementary ... See full document

... of domination in graphs was introduced by ...the domination number of G and is denoted by  ...of complementary tree dominating ...a complementary tree dominating set (ctd-set), ... See full document

... 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 ... See full document

... the domination number of G, it is denoted by ...a perfect dominating set if for every vertex 𝑣 ∈ 𝑉/𝑆, there exists exactly one vertex 𝑤 ∈ 𝑆 such that 𝑣𝑤 ∈ 𝐸; that is every vertex outside S has ... See full document

... In this paper we consider simple, connected and bipartite graphs. All notations and definitions not given here can be found in [1, 3]. A graph is an ordered pair G = ( V ( G ) , E ( G )) , where V ( G ) is a ... See full document

... of domination in graphs evolved from a chess board problem known as the Queen problem- to find the minimum number of queens needed on an 8x8 chess board such that each square is either occupied or ... See full document

... and domination numbers for block-cactus graphs having π(G) induced cycles of length 2 (mod ...block-cactus graphs can be found in [6, 8, 9, ... See full document

... In this paper, we initiate the study of an edge Roman star domination function(ERSDF, for short) which is an extension of an edge Roman domination function. Here, we add one extra condition that the sum of ... 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

... in graphs has become an important area of research in graphs as evidenced by the many results contained in two books by Haynes, Hedetniemi and Slater (1998) ...connected graphs. The concept of triple ... See full document