A PROPERLY EVEN HARMONIOUS LABELING OF SOME WHEEL GRAPH Wn FOR n IS EVEN

Abstract

A properly even harmonious labeling of a graph G with q edges is an injective mapping f from the vertices of graph G to the integers from 0 to 2q − 1 such that induces a bijective mapping f* from the edges of G to {0,2, …,2q − 2} defined by f*(vi vj) = (f(vi) + f(vj))(mod2q). A graph that has a properly even harmonious labeling is called a properly even harmonious graph. In this research, we will show the existence of a properly even harmonious labeling of some wheel graph Wn for n is even.