Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Gallai and Anti-Gallai Graphs of Strongly Regular Graphs

  • Jeepamol J. Palathingal (Department of Mathematics, PM Government College) ;
  • Aparna Lakshmanan S. (Department of Mathematics, Cochin University of Science and Technology) ;
  • Greg Markowsky (School of Mathematics, Monash University)
  • Received : 2023.01.08
  • Accepted : 2023.11.03
  • Published : 2024.03.31
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Abstract

In this paper, we show that if G is strongly regular then the Gallai graph Γ(G) and the anti-Gallai graph ∆(G) of G are edge-regular. We also identify conditions under which the Gallai and anti-Gallai graphs are themselves strongly regular, as well as conditions under which they are 2-connected. We include also a number of concrete examples and a discussion of spectral properties of the Gallai and anti-Gallai graphs.

Keywords

Acknowledgement

We would like to thank Misha Lavrov for helpful conversations, and an anonymous referee for useful comments.

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