On local distance antimagic labeling of graphs

Abstract

AbstractLet [Formula: see text] be a graph of order n and let [Formula: see text] be a bijection. For every vertex [Formula: see text], we define the weight of the vertex v as [Formula: see text] where N(v) is the open neighborhood of the vertex v. The bijection f is said to be a local distance antimagic labeling of G if [Formula: see text] for every pair of adjacent vertices [Formula: see text]. The local distance antimagic labeling f defines a proper vertex coloring of the graph G, where the vertex v is assigned the color w(v). We define the local distance antimagic chromatic number [Formula: see text] to be the minimum number of colors taken over all colorings induced by local distance antimagic labelings of G. In this paper we obtain the local distance antimagic labelings for several families of graphs including the path Pn, the cycle Cn, the wheel graph Wn, friendship graph Fn, the corona product of graphs [Formula: see text], complete multipartite graph and some special types of the caterpillars. We also find upper bounds for the local distance antimagic chromatic number for these families of graphs.

Keywords

• Distance magic graphs
• local distance antimagic labeling
• local distance antimagic chromatic number
• 05C 78