VERTEX - EDGE DOMINATING COLORING OF GRAPHS

A vertex $u$ in a graph G = (V,E) is said to {ve-dominate} an edge $e = vw$ if $u \in \{v, w\}$ or $uv \in E(G)$ or $uw \in E(G)$. An edge coloring is said to be a $ve$ - dominating coloring if no two edges $ve$ - dominated by a single vertex receive the same color. The minimum number of colors required for a $ve$ - dominating coloring of a graph G is called {ve - chromatic number} of G and is denoted by $\chi_{ve}(G)$. In this paper we initiate the study of this parameter.