Spectrum of anti-gallai graph of some graphs

Jeepamol J. Palathingal (), Aparna S. Lakshmanan () and Gopalapillai Indulal ()
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Jeepamol J. Palathingal: PM Government College
Aparna S. Lakshmanan: Cochin University of Science and Technology
Gopalapillai Indulal: St. Aloysius College

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 304-311

Abstract: Abstract The anti-Gallai graph $$\Delta (G)$$ Δ ( G ) of a graph G, has the edges of G as its vertices and two distinct edges are adjacent in $$\Delta (G)$$ Δ ( G ) if they lie on a triangle in G. In this paper we characterize the graphs whose anti-Gallai graph has only one or two eigenvalues and study the adjacency spectrum of the anti-Gallai graph of $$(K_4,H)$$ ( K 4 , H ) -free graphs, where H is the Hajos graph and graphs in which two diamonds share at most one vertex. We also find expressions for the adjacency spectrum of anti-Gallai graph of graphs after applying certain binary operations.

Keywords: Line graph; Anti- Gallai graph; Adjacency matrix; Adjacency spectrum; Binary operations in graph; 05C05; 15A42; 05C76 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00066-z

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