Antimagicness of Tensor product for some wheel related graphs with star

TL;DR

This paper proves that the tensor product of certain wheel-related graphs with a star graph is antimagic, supporting the broader conjecture that all connected graphs are antimagic except for P2.

Contribution

It establishes antimagicness for tensor products of wheel, helm, and flower graphs with a star, advancing the understanding of the antimagic graph conjecture.

Findings

Tensor product of wheel and star is antimagic.

Tensor product of helm and star is antimagic.

Tensor product of flower and star is antimagic.

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.