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 $\{1,2,\dots ,|E(G)|\}$, 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.