On Odd Harmonious Labeling of m-Shadow of Cycle, Gear with Pendant and Shuriken Graphs

摘要

A graph G = (V (G),E (G)) with p vertices and q edges is called (p, q)-graph. An injection f is said to be odd harmonious labeling of a (p, q)-graph G if there is an injective function f from a set of vertices V(G) to a set {0, 1, 2, ..., 2q - 1} such that the induced function f* from a set of edges E(G) to a set of odd number {1, 3, 5,. .. 2q- 1} defined by f* (uv) = f (u) + f (v) is a bijection. A graph G is said to be odd harmonious if there exists an odd harmonious labeling for G. In this paper we proved that several product graphs, such as m-shadow of cycle D_m (C_n), gear with pendant graphs and Shuriken graphs, are odd harmonious graphs.