Complementary Tree Domination Number of Corona Product of Complete graph with Some Graphs

Abstract

A set D of a graph  G  =  (V, E)  is  a  dominating  set,  if  every vertex in V − D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. A dominating set D is called a complementary tree dominating set if the induced subgraph <V  − D> is a tree.  The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of G and is denoted by γctd(G). The corona G1 ◦ G2 of two graphs G1 and G2 are defined as the graph G obtained by taking one copy of G1 of order p1 and p1 copies of G2 and then joining the ith vertex of G1 to every vertex in the ith copy of G2. The corona G1 ◦ G2 has p1(1 + p2) vertices and q1 + p1q2 + p1p2 edges. In this paper, we discussed complementary tree domination number of corona product of complete graph with some graphs.