@article{Rather2022, 
author = {Bilal A. Rather and M. Aijaz and Fawad Ali and Nabil Mlaiki and Asad Ullah},
title = {On distance signless Laplacian eigenvalues of zero divisor graph of commutative rings},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {7},
pages = {12635-12649},
keywords = {distance signless Laplacian matrix, zero divisor graphs, commutative rings, trace norm},
url = {https://www.sciopen.com/article/10.3934/math.2022699},
doi = {10.3934/math.2022699},
abstract = {For a simple connected graph    G of order    n, the distance signless Laplacian matrix is defined by        D          Q        (  G  )  =  D  (  G  )  +  T  r  (  G  ), where    D  (  G  ) and    T  r  (  G  ) is the distance matrix and the diagonal matrix of vertex transmission degrees, respectively. The zero divisor graph    Γ  (  R  ) of a finite commutative ring    R is a simple graph, whose vertex set is the set of non-zero zero divisors of    R and two vertices    v  ,  w  ∈  Γ  (  R  ) are edge connected whenever    v  w  =  w  v  =  0. In this article, we find the        D          Q      -eigenvalues of zero divisor graph of the ring              Z              n       for general value    n  =            p              1                              l                      1                                      p              2                              l                      2                              , where        p    1    <      p    2   are distinct prime numbers and        l          1        ,      l          2        ∈      N  . Further, we investigate the        D          Q      -eigenvalues of zero divisor graphs of local rings and the rings whose associated zero divisor graphs are Hamiltonian. Also, we obtain the trace norm and the Wiener index of    Γ  (            Z              n        ) for some special values of    n.}
}