Odd Harmonious Labeling of Some Graphs

Abstract

The labeling of discrete structures is a potential area of research due to its wide range of applications. The present work is focused on one such labeling called odd harmonious labeling. A graph G is said to be odd harmonious if there exist an injection f : V (G) → {0,1,2,...,2q − 1} such that the induced function f ∗ : E(G) → {1,3,...,2q − 1} defined by f ∗ (uv) = f(u)+f(v) is a bijection. Here we investigate odd harmonious labeling of some graphs. We prove that the shadow graph and the splitting graph of bistar Bn,n are odd harmonious graphs. Moreover we show that the arbitrary supersubdivision of path Pn admits odd harmonious labeling. We also prove that the joint sum of two copies of cycle Cn for n ≡ 0(mod 4) and the graph Hn,n are odd harmonious graphs.