Odd Harmonious Labeling of Some New Families of Graphs

Abstract

A graph G 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)(mod2q) is a bijection. A graph that admits odd harmonious labeling is called odd harmonious graph. In this paper we prove that the shadow and splitting of graph K2,n, Cn for n≡0(mod4), the graph Hn,n and double quadrilateral snakes DQ(n), n≥2 are odd harmonious graphs.