Families of Non-Even Harmonious Graphs

A graph of size 2q is even harmonious if its vertices can be labeled distinctly from the labels 0,1,2,...,2q-2 such that the set of edge labels obtained by adding the vertex labels modulo 2q is {2k, 2k+2,..., 2k+2q-2}. Proving that a graph is not even harmonious is not an easy task. In this paper, we give some families of non-even harmonious graphs.