Laplacian eigenvalues of the unit graph of the ring Zn

Shouqiang Shen, Weijun Liu and Wei Jin

Applied Mathematics and Computation, 2023, vol. 459, issue C

Abstract: We investigate the Laplacian eigenvalues about unit graph G(Zn) on Zn and show the case whenever n is an even number or an odd prime power, G(Zn) would be Laplacian integral. We also prove that if n>1, then the Laplacian spectral radius of G(Zn) is equal cardinal number of V(G(Zn)) if and only if n=pk, here p is a prime integer, k is an integer that positive. In addition, this paper also characterizes n that algebraic connectivity of G(Zn) coincides with the vertex connectivity.

Keywords: Unit graph; Laplacian spectral radius; Algebraic connectivity; Vertex connectivity (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:459:y:2023:i:c:s009630032300437x

DOI: 10.1016/j.amc.2023.128268

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