English

Antimagicness of Tensor product for some wheel related graphs with star

Combinatorics 2024-05-08 v4

Abstract

A graph GG with pp vertices and qq edges has an antimagic labelling if there is a bijection from the graph's edge set to the label set {1,2,,q}\left\{1,2, \cdots, q \right\} such that pp vertices must have distinct vertex sums, where the vertex sums are determined by adding up all the edge labels incident to each vertex vv in V(G)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 P2P_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.

Keywords

Cite

@article{arxiv.2310.07114,
  title  = {Antimagicness of Tensor product for some wheel related graphs with star},
  author = {Vinothkumar Latchoumanane and Murugan Varadhan},
  journal= {arXiv preprint arXiv:2310.07114},
  year   = {2024}
}

Comments

28 pages, 3 figures