Even vertex odd mean labeling of graphs

Abstract

In this paper we introduce a new type of labeling known as even vertex odd mean labeling. A graph $G$ with $p$ vertices and $q$ edges is said to have an even vertex odd mean labeling if there exists an injective function $f:V(G)\to \{0,2,4,\dots ,2q-2,2q\}$ such that the induced map $f^{\ast }:E(G)\to \{1,3,5,\dots ,2q-1\}$ defined by $f^{\ast }(uv)=\frac{f(u)+f(v)}{2}$ is a bijection. A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. Here we investigate the even vertex odd mean behaviour of some standard graphs.