[PDF] Top 20 Domination parameters of split graphs

... The concept of domination in graphs began in the mid of 1860s with the game of chess. The goal of the problem was to use certain chess pieces to dominate the squares of the chess board. Knowing that a queen ... See full document

... By a graph G = (V,E) we mean a finite, undirected graph with neither loops nor multiple edges. The order and size of G are denoted by p and q respectively. For graph theoretic terminology we refer to Chartrand and ... See full document

... in graphs has been an extensively research branch of graph ...Cayley graphs are excellent models for interconnection networks, investigated in connection with parallel processing and distributed ... See full document

... Cayley graphs as a model for developing interconnection net- works for large interacting arrays of ...Cayley graphs can be found in [1]. The concept of domination for Cayley graphs has been ... See full document

... Let G = (V,E) be a graph, and let g be a function that assigns to each edge a set of colors chosen from the power set of {1,2} that is, g:E(G)→ {1,2}. If for each edge E(G) such that g( we have ⋃ = {1,2}, then g is ... See full document

... The neighbourhoodnumber[1] of G is defined as the minimum cardinality of a neighbourhood set of G . A vertex in a graph G dominates itself and its neighbours. A subset D of V is said to be a dominating set of G if every ... See full document

... Roman domination is introduced by ...of domination and its parameters dependent, determine the graph that is the number of that parameter is ...all graphs with total domination number ... See full document

... detour graphs were introduced and studied in [7]. A split (G,D)-set S of a graph G is said to be a split (G,D)-set of G if the subgraph induced by V – S is ...strong split (G,D)-set of G if ... See full document

... of domination number in graphs called hn- domination number denoted by 𝛾 ℎ𝑛 ...these parameters are determined, specifically, the impact on hn-domination parameter is studied thoroughly ... See full document

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

... Abstract: For any graph = ( , ), the Lict graph ( ) of a graph is a graph whose set of vertices is the union of the set of edges and cutvertices of in which two vertices are adjacent if and only if the corresponding ... See full document

... standard graphs were also ...different domination parameters were obtained. Also we relate split domination and end edge domination numbers in G ... See full document

... Proposition 3.23. For any bipolar fuzzy graph (BFG) G = $σ, μ s , μ t % , γ cc (G) ≤ β(G) Proof: Let D be a maximal independent set of bipolar fuzzy vertex in G , then G has atleast two bipolar fuzzy vertices and every ... See full document

... the Split complement line domonation ...the Split domination concept for the complement of line graph and defined Split complement line domination number for the graph ... See full document

... Swaminathan et al [13] introduced the concept of equitable domination in graph by considering the following real world problems. In a network, nodes with nearly equal capacity may interact with each other in a ... See full document

... All graphs will be finite and undirected without multiple edges. If G is a graph, V (G) denotes the set, and |G| the number, of vertices in G. Let N (x) denote the neighborhood of a vertex x, and let hXi denote ... See full document

... 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 of a ... See full document

... Abstract. A dominating set D of an IFG G = (V, E) is a non-split dominating set, if the induced intuitionistic fuzzy subgraph 〈 − 〉 is connected. The Non-split domination number of IFG G is the ... See full document

... Important results on characterization of non-split and inverse non-split dominating sets were presented here and corresponding formulas for computing the non-split and inverse non-split [r] ... See full document

... equitable domination number of G which is denoted by γ e ...equitable domination number of G is the minimum cardinality of a total equitable dominating set of G which is denoted by γ t e ...equitable ... See full document