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,  are harmonious graphs.