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Switching Methods of Level 2 for the Construction of Cospectral Graphs by Abiad, Aida; van de Berg, Nils; Simoens, Robin is a scholarly article available to read on EtoBox.

What is Switching Methods of Level 2 for the Construction of Cospectral Graphs about?

A switching method is a graph operation that results in cospectral graphs (graphs with the same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most cospectral graphs with cospectral complements can be constructed using regular orthogonal matrices of level 2, which has relevance for Haemers' conjecture. We present two new switching methods and several combinatorial and geometrical reformulations of existing switching operations of level 2. We also introduce the concept of reducibility and use it to classify all irreducible switching methods that correspond to a conjugation with a regular orthogonal matrix of level 2 with one nontrivial indecomposable block, up to switching sets of size 12, extending previous results.

Author

Abiad, Aida; van de Berg, Nils; Simoens, Robin

Published

2024

Language

EN