Generalization of graphs Randič? energy

In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998) 199–206). A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S ...

Let G be a simple graph with vertex set V ( G ) = { v 1 , v 2 , , v n } . The Randić matrix of G, denoted by R(G), is defined as the n n matrix whose (i, j)-entry is ( d i d j ) - 1 2 if vi and vj are adjacent and 0 for another cases. Let the ...

A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γ_t(G) of G. It is known [J Graph Theory 35 (2000),...