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The Gallai and Anti-Gallai Graphs of Strongly Regular Graphs
Jeepamol J. Palathingal,Aparna Lakshmanan S.,Greg Markowsky 경북대학교 자연과학대학 수학과 2024 Kyungpook mathematical journal Vol.64 No.1
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.