• 제목/요약/키워드: Anti-Gallai graph

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The Gallai and Anti-Gallai Graphs of Strongly Regular Graphs

  • Jeepamol J. Palathingal;Aparna Lakshmanan S.;Greg Markowsky
    • Kyungpook Mathematical Journal
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    • 제64권1호
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    • pp.171-184
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    • 2024
  • 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.