Minus Edge Domination in Graphs

Abstract

Let ${\gamma }_{\overline{E}}$ and ${\gamma }_{\overline{S}}$ be the minus edge domination and minus star domination numbers of a graph, respectively, and let ${\gamma }_E$, ${\beta }_1$, ${\alpha }_1$ be the edge domination, matching, and edge covering numbers of a graph. In this paper, we present some bounds on ${\gamma }_{\overline{E}}$ and ${\gamma }_{\overline{S}}$ and characterize the extremal graphs of even order $n$ attaining the upper bound $\frac{n}{2}$ on ${\gamma }_{\overline{E}}$. We also investigate the relationships between the above parameters.