Some Classes of Antimagic Graphs with Regular Subgraphs

Abstract

A labeling f of a graph G is a bijection from its edge set \(E(G)\) to the set \(\{1, 2, …, |E(G)|\}\), which is antimagic if for any distinct vertices \(x\) and \(y\), the sum of the labels on edges incident to \(x\) is different from the sum of the labels on edges incident to \(y\). A graph G is antimagic if \(G\) has an f which is antimagic. Hartsfield and Ringel conjectured in \(1990\)
that every connected graph other than Ko is antimagic. In this paper, we show that some graphs with regular subgraphs are antimagic.