Elegant labeling of sun graphs and helm graphs

Abstract

Let G be a simple and finite graph having q edges. An elegant labeling f of G is an injective function from the set of vertices of G to the set {0,1,2,⋯,q} such that the induced edge labels, where each edge xy is assigned the label f∗(xy) = f(x) + f(y) (mod(q + 1)), are distinct and non zero. If a graph can be labeled by an elegant labeling, then the graph is said to be elegant. In this paper we show that sun graph n-sun and helm graph Hn, where n is an odd integer at least 3, are elegant.