Odd harmonious labeling of some cycle related graphs

Abstract

A graph G(p, q) is said to be odd harmonious if there exists 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. 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.