Changing and Unchanging of Complementary Tree Domination Number in 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 $\gamma(G)$ 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 $ $ 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 $\gamma_{ctd}(G)$. The concept of complementary tree domination number in graphs is studied in \cite{a}. In this paper, we have studied the changing and unchanging of complementary tree domination number in graphs.