H-integral and Gaussian integral normal mixed Cayley graphs

2021/10/07 by Monu Kadyan, Kadyan, Monu, Bhattacharjya, Bikash · 1 citation
Mathematics · #05C25 #05C50 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2110.03268

openalex publication_date 2021/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If all the eigenvalues of the Hermitian-adjacency matrix of a mixed graph are integers, then the mixed graph is called H-integral. If all the eigenvalues of the (0,1)-adjacency matrix of a mixed graph are Gaussian integers, then the mixed graph is called Gaussian integral. For any finite group Γ, we characterize the set S for which the normal mixed Cayley graph Cay(Γ, S) is H-integral. We further prove that a normal mixed Cayley graph is H-integral if and only if it is Gaussian integral.

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