Spectrum of Strongly Regular Graphs under Graph Operators
Jeepamol J Palathingal, Aparna Lakshmanan S, Greg Markowsky
TL;DR
This paper investigates the properties of Gallai and anti-Gallai graphs derived from strongly regular graphs, revealing conditions for their regularity, connectivity, and spectral characteristics.
Contribution
It establishes new conditions under which Gallai and anti-Gallai graphs of strongly regular graphs are strongly regular or 2-connected, and explores their spectral properties.
Findings
Gallai and anti-Gallai graphs of strongly regular graphs are edge-regular.
Conditions identified for these graphs to be strongly regular.
Spectral properties of Gallai and anti-Gallai graphs are discussed.
Abstract
In this paper, we show that if G is strongly regular then the Gallai graph and the anti-Gallai graph 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.
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Taxonomy
TopicsFinite Group Theory Research · Graph theory and applications · Advanced Topics in Algebra