Antimagicness of Tensor product for some wheel related graphs with star

Abstract

A graph $G$ with $p$ vertices and $q$ edges has an antimagic labelling if there is a bijection from the graph's edge set to the label set $\left\{1,2, \cdots, q \right\}$ such that $p$ vertices must have distinct vertex sums, where the vertex sums are determined by adding up all the edge labels incident to each vertex $v$ in $V(G)$. Hartsfield and Ringel \cite{Ringel1} in the book "Pearls in Graph Theory" conjectured that every connected graph is antimagic, with the exception of $P_2$. In this study, we identified a class of connected graphs that lend credence to the conjecture. In this article, we proved that the tensor product of a wheel and a star, a helm and a star, and a flower and a star is antimagic.