ON THE RELATIONS BETWEEN THE PARAMETERS OF GRAPHS

Abstract

Let $G(V,E)$ be a graph of order $p$. Denote by $\sigma(G)$, $\sigma_1(G)$, $\alpha_T(G)$ and $\beta_T(G)$ the dominating number, the edge dominating number, the total covering number and the total independence number of $G(V,E)$, respectively. Let $\overline{G}$ denote the complement graph of $G$. This paper establishes some relations among $\sigma(G)$, $\beta_T(G)$, $\alpha_T(G)$, $\sigma_1(G)$, $\sigma(\overline{G})$ and $\sigma_1(\overline{G})$.