Open AccessOn Laplacian spectrum of unitary Cayley graphs
Author(s) -
S. Pirzada,
Zahra Barati,
Mojgan Afkhami
Publication year - 2021
Publication title -
acta universitatis sapientiae. informatica
Language(s) - English
Resource type - Journals
eISSN - 2066-7760
pISSN - 1844-6086
DOI - 10.2478/ausi-2021-0011
Subject(s) - cayley graph , combinatorics , mathematics , unitary state , vertex (graph theory) , simple graph , commutative ring , laplacian matrix , laplace operator , graph , vertex transitive graph , discrete mathematics , eigenvalues and eigenvectors , line graph , voltage graph , commutative property , physics , mathematical analysis , political science , law , quantum mechanics
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 G R = 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 G R and its line graph.