Odd harmonious labeling of some new families of 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 shadow and splitting of graph K2,n,Cn for n≡0 (mod 4), the graph Hn,n, double quadrilateral snakes DQ(n),n≥2, the graph Pr,m if m is odd, banana tree and the path union of cycles Cn for n≡0 (mod 4) are odd harmonious.