New results on odd harmonious labeling of graphs

Abstract

Let G = (V, E) be a graph with p vertices and q edges. 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) is a bijection. If f(V (G)) = {0, 1, 2, · · · , q} then f is called strongly odd harmonious labeling and the graph is called strongly odd harmonious graph. In this paper we prove that Spl(Cbn) and Spl(B(m)(n)), slanting ladder SLn, mGn, H-super subdivision of path Pn and cycle Cn, n ? 0(mod 4) admit odd harmonious labeling. In addition we observe that all strongly odd harmonious graphs admit mean labeling, odd mean labeling, odd sequential labeling and all odd sequential graphs are odd harmonious and all odd harmonious graphs are even sequential harmonious.