<abstract xmlns="http://www.w3.org/1999/xhtml">

Let R be a commutative ring with unity 1 ≠ 0 and let R× be the set of all unit elements of R. The unitary Cayley graph of R, denoted by GR = Cay(R, R×), is a simple graph whose vertex set is R and there is an edge between two distinct vertices x and y of R if and only if x − y ∈ R×. In this paper, we determine the Laplacian and signless Laplacian eigenvalues for the unitary Cayley graph of a commutative ring. Also, we compute the Laplacian and signless Laplacian energy of the graph GR and its line graph.
</abstract>

Let R be a commutative ring with unity 1 ≠ 0 and let R× be the set of all unit elements of R. The unitary Cayley graph of R, denoted by GR = Cay(R, R×), is a simple graph whose vertex set is R and there is an edge between two distinct vertices x and y of R if and only if x − y ∈ R×. In this paper, we determine the Laplacian and signless Laplacian eigenvalues for the unitary Cayley graph of a commutative ring. Also, we compute the Laplacian and signless Laplacian energy of the graph GR and its line graph.

On Laplacian spectrum of unitary Cayley graphs

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"On Laplacian spectrum of unitary Cayley graphs"}

Let R be a commutative ring with unity 1 ≠ 0 and let R× be the set of all unit elements of R. The unitary Cayley graph of R, denoted by GR = Cay(R, R×), is a...

On Laplacian spectrum of unitary Cayley graphs

Published Online: Feb 02, 2022

Page range: 251 - 264

Received: Oct 04, 2021

Accepted: Oct 11, 2021

DOI: https://doi.org/10.2478/ausi-2021-0011

© 2021 S. Pirzada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.