Odd harmonious labeling of some cycle related graphs

Abstract

A graph G(p, q) is said to be odd harmonious if there exists an in-jection 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. A graph that admits odd harmonious labeling is called odd harmonious graph. In this paper we prove that any two even cycles sharing a common vertex and a common edge are odd harmonious graphs.