A new class of disconnected antimagic graphs

Abstract

A graph G is antimagic if there exists a bijection f from E(G) to {1, 2, . . . , |E(G)|} such that the vertex sums for all vertices of G are distinct, where the vertex sum is defined as the sum of the labels of all incident edges. Hartsfield and Ringel conjectured that every connected graph other than K_2 admits an antimagic labeling. It is still a challenging problem to address antimagicness in the case of disconnected graphs. In this paper, we study antimagicness for the disconnected graph that is constructed as the direct product of a star and a path.