Even-Odd Harmonious Graphs

A graph G(V, E) with n vertices and m edges is said to be even-odd harmonious if there exists an injection f : V(G) →{ 1, 3, 5,…, 2n-1} such that the induced mapping f *:E(G) → {0,2,4,…,2(m-1)} defined by f*(uv) = [f(u) + f(v)] (mod 2m) is a bijection. The function f is called even-odd harmonious labeling of G. In this paper, we prove that the bistar graph Bm,n, cycle with one pendent edge, crown graph, the graph K1,m,n. the prism graph C3Yn and the graph nP2 are even-odd harmonious graphs.