Antimagic Labeling for Product of Regular Graphs

Abstract

An antimagic labeling of a graph G=(V,E) is a bijection from the set of edges of G to 1,2,⋯,E(G) and such that any two vertices of G have distinct vertex sums where the vertex sum of a vertex v in V(G) is nothing but the sum of all the incident edge labeling of G. In this paper, we discussed the antimagicness of rooted product and corona product of graphs. We proved that if we let G be a connected t-regular graph and H be a connected k-regular graph, then the rooted product of graph G and H admits antimagic labeling if t≥k. Moreover, we proved that if we let G be a connected t-regular graph and H be a connected k-regular graph, then the corona product of graph G and H admits antimagic labeling for all t,k≥2.