On Harmonious Graphs

Abstract

Let G = (V (G), E(G)) be a graph with q edges. A function f is called harmonious labeling of graph G if f: V →¨{0, 1, 2,…, q-1} is injective and the induced function f*: E → {0, 1, 2,…, q} defined as f*(uv) = (f(u) + f(v))(mod q) is bijective. A graph which admits harmonious labeling is called harmonious graph. In this paper we prove that the jewel graph, triangular ladder graph, special flower graph, duplicating all the vertex of mK1, in P2+mK1, T(Pn)Kcm are harmonious graphs.