CHARACTERIZATION OF GRAPHS WITH EQUAL DOMINATION NUMBERS AND INDEPENDENCE NUMBERS

Abstract

The domination number $\gamma(G)$ of a graph $G$ is the minimum cardinality among all dominating sets of $G$, and the independence number $\alpha(G)$ of $G$ is the maximum cardinality among all independent sets of $G$. For any graph $G$, it is easy to see that $\gamma(G) \leq \alpha(G)$. Jou [6] has characterized trees with equal domination numbers and independence numbers. In this paper, we extend the result and present a characterization of connected unicyclic graphs with equal domination numbers and independence numbers.