Antimagicness for tensor product of wheel and star

Andrea Semaničová-Feňovčíková, Vinothkumar Latchoumanane, Murugan Varadhan

Published 2023-10-11Version 1

An antimagic labeling for a graph $G$ with $p$ vertices and $q$ edges is a bijection from the edge set of a graph G to the label set $\left\{1,2, \cdots, q \right\}$ such that $p$ vertices must have distinct vertex sums, whereas the vertex sums are calculated by summing all the edge labels incident to each vertex $v \in V$. Every connected graph, with the exception of $K_2$, is antimagic, conjectured by Hartsfield and Ringel \cite{Ringel1} in the book called "Pearls in Graph Theory". In this paper, we found a class of connected graph for supporting the conjecture. That is, the tensor product of wheel and star is antimagic.