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arXiv · 2310.07114

Antimagicness of Tensor product for some wheel related graphs with star

Vinothkumar Latchoumanane·Murugan Varadhan
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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.

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Vinothkumar Latchoumanane, Murugan Varadhan. 2023-10-11. Antimagicness of Tensor product for some wheel related graphs with star. https://arxiv.org/abs/2310.07114

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