On Even-to-Odd Mean Labeling of Some Trees

Abstract

Let G=(V(G), E(G)) be a connected graph with order |V(G)|=p and size |E(G)|=q. A graph G is said to be even-to-odd mean graph if there exists a bijection function phi:V(G) to {2, 4, ..., 2p} such that the induced mapping phi^*:E(G) to {3, 5, ..., 2p-1} defined by phi^*(uv)=[phi(u)+phi(v)]/2 for all uv element of E(G) is also bijective. The function is called an even-to-odd mean labeling of graph . This paper aimed to introduce a new technique in graph labeling. Hence, the concepts of even-to-odd mean labeling has been evaluated for some trees. In addition, we examined some properties of tree graphs that admits even-to-odd mean labeling and discussed some important results.