Odd Harmonious Labeling on Pleated of the Dutch Windmill Graphs

Abstract

A graph G(p,q) with p=|V(G)| vertices and q=|E(G)| edges. The graph G(p,q) 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)-{1,2,3,...,2q-1} defined by  f*(uv)=f(u)+f(v) which is a bijection and f is said to be odd harmonious labeling of G(p,q). In this paper we prove that pleated of the Dutch windmill graphs C_4^(k)(r) with k=1 and r=1 are odd harmonious graph. Moreover, we also give odd harmonious labeling construction for the union pleated of the Dutch windmill graph   C_4^(k)(r) union C_4^(k)(r) with k=1 and r=1.