@article{Fakieh2024, 
author = {Wafaa Fakieh and Amal Alsaluli and Hanaa Alashwali},
title = {Laplacian spectrum of the unit graph associated to the ring of integers modulo    p  q},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {4098-4108},
keywords = {unit graph, Laplacian matrix, Laplacian spectrum, direct product, ring of integers modulo n},
url = {https://www.sciopen.com/article/10.3934/math.2024200},
doi = {10.3934/math.2024200},
abstract = {Let    R be a ring and    U  (  R  ) be the set of unit elements of    R. The unit graph    G  (  R  ) of    R is the graph whose vertices are all the elements of    R, defining distinct vertices    x and    y to be adjacent if and only if    x  +  y  ∈  U  (  R  ). The Laplacian spectrum of    G  (            Z        n    ) was studied when    n  =      p          m      , where    p is a prime and    m is a positive integer. Consequently, in this paper, we study the Laplacian spectrum of    G  (            Z        n    ), for    n  =      p    1        p    2    .  .  .      p    k  , where        p    i   are distinct primes and    i  =  1  ,  2  ,  .  .  .  ,  k.}
}