Even -odd average harmonious graph

Abstract

This article studies we have presented an innovative harmonious labelling is Even odd average harmonious graph labeling. G is an Even odd average harmonic graph because it contains n vertices and m edges if such a function exists f:V(G)→{1,3,5,⋯(2n-1)} as the induced mapping f∗:E(G)→0,1,2,⋯.m-1} characterized as f∗(uv) = fu+f(v)2 (modm) is a bijection. The function fis said to be an Even the odd average harmonious graph G. A graph which admit an Even the odd average harmonious graph. We demonstrated in this research that the graph path Pn, cycle Cn, the star graph Sq+1, the graph Pn2, the bistar graph Bp,q, the comb Pr⊙K1, the graph C3@pK1, the graph C2r-1@K1 are even odd Average Harmonious Labeling of graphs.