Spectral properties of Cayley graphs over finite commutative rings

2024/06/23 by Sanjay Kumar Singh, Priya, Singh, Sanjay Kumar · 1 citation
Mathematics · #05C50 #20C25 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2406.16080

openalex publication_date 2024/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a finite commutative ring with unity and x be a non-zero element of R. In this paper, we calculate the spectrum and energy of the Cayley graph \rm Cay(R,xR^*), and also compute the energy of their compliment graph. Further, we give necessary and sufficient condition for Cayley graph \rm Cay(R,xR^*) to be Ramanujan.

Cited by

• A generalization of Ramanujan's sum over finite rings

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