Spectra of the zero-divisor graph of finite rings

2021/06/30 by Masalkar, Krishnat D., Khairnar, Anil, Lande, Anita +1
#15A18 #FOS: Mathematics #Primary: 05C25 #Secondary: 05C50 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2106.15977

Abstract

The zero-divisor graph Γ(R) of a ring R is a graph with nonzero zero-divisors of R as vertices and distinct vertices x,y are adjacent if xy=0 or yx=0. We provide an equivalence relation on a ring R and express Γ(R) as a generalized join of graphs on equivalence classes of this relation. We determined the adjacency and Lapalcian spectra of Γ(R) when R is a finite semisimple ring.

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