Forbidden subgraphs of Co-prime graphs of finite groups

Document Type : Research Paper

Authors

Department of Mathematics, National Institute of Technology Calicut, P.O.Box 673601, Calicut, India

10.22108/toc.2024.137172.2055

Abstract

For a finite group $G$ the co-prime graph $\Gamma(G)$ is defined as a graph with vertex set $G$ in which two distinct vertices $x$ and $y$ are adjacent if and only if $gcd(o(x),o(y))=1$ where $o(x)$ and $o(y)$ denote the orders of the elements $x$ and $y$ respectively. In this paper we find properties of groups whose co-prime graphs forbid graphs such as $C_4,K_{1,3},P_4$ and asteroidal triples.

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References

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Transactions on Combinatorics

Articles in Press, Corrected Proof
Available Online from 18 August 2024

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History

  • Receive Date: 23 March 2023
  • Revise Date: 11 June 2024
  • Accept Date: 15 June 2024
  • Published Online: 18 August 2024

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