A graph G is dot-critical if contracting any edge decreases the domination number. It is totally dot-critical if identifying any two vertices decreases the domination number. Burton and Sumner… (More)

In this paper, we study the Goldberg Snarks Gk, twist Goldberg Snarks TGk, Flower snarks Fk, and show the exact value of connected and tree domination number of them. Mathematics Subject… (More)

Let (G) be the domination number of graph G, thus a graph G is k -edge-critical if (G) 1⁄4 k ; and for every nonadjacent pair of vertices u and v, (Gþ uv) 1⁄4 k 1. In Chapter 16 of the book… (More)

A dominator coloring of a graph G is a proper coloring of G with the additional property that every vertex dominates an entire color class. The dominator chromatic number χd(G) of G is the minimum… (More)

A set S of vertices in a graph G is a double total dominating set, abbreviated DTDS, of G if every vertex of G is adjacent to least two vertices in S. The minimum cardinality of a DTDS of G is the… (More)