On Harmonious Labelings of Some Cycle Related Graphs

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.