An Algorithmic Approach to Antimagic Labeling of Edge Corona Graphs

Abstract

An antimagic labeling of a graph $G$ is a $1-1$ correspondence between the edge set $E(G)$ and $\lbrace 1,2,...,|E(G)|\rbrace$ in which the sum of the labels of edges incident to the distinct vertices are different. The edge corona of any two graphs $G$ and $H$, (denoted by $G$ $\diamond$ $H$) is obtained by joining one copy of $G$ with $|E(G)|$ copies of H such that the end vertices of $i^{th}$ edge of $G$ is adjacent to every vertex in the $i^{th}$ copy of $H$. In this paper, we provide an algorithm to prove that the following graphs admit an antimagic labeling: $-$ $n$-barbell graph $B_n$, $n\geq3$ $-$ edge corona of a bistar graph $B_{x,n}$ and a $k$-regular graph $H$ denoted by $B_{x,n}\diamond H$, $x,n\geq 2$ $-$ edge corona of a cycle $C_m$ and $C_n$ denoted by $C_m \diamond C_n$, $m,n\geq3$