Collections Of Statements Related To Domination Parameters In Graphs

Source abstract

Mathematical structures are used to model pairwise relations between objects from a certain collection. A "graph" in this context, refers to a collection of vertices V (G) or 'nodes' and a collection of edges E (G) that connect pairs of vertices. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another. In this , the authors collect the basic definitions on graphs which are related to the Nilprivate neighbour domination and strong non-split domination. A set D V is a dominating set of a graph G if each vertex of V-D is adjacent to atleast one vertex in S. A dominating set S in G is a minimal dominating set, if no proper subset S S is domination set of G. The domination number is the minimum cardinality 1 of a minimal dominating set in G and is denoted by (G) or simply . Every maximal independent set in a graph G is a minimal dominating set of G. An independent set S V is maximal independent, if and only if, it is independent and dominating (Haynes, Hedetniemi, & Slater, 1998). A dominating set D of a graph G=(V, E) is a maximal dominating set if V-D is not a dominating set of G. The maximal domination number (G) is the minimum cardinality of a maximal dominating set of G. A minimal dominating set D of a m graph G is a maximal dominating set, if and only if, G contains an isolated vertex.