For a finite group G and a subset X∅ of G, the commuting graph, indicated by G= C (G, X), is
the simple connected graph with vertex set X and two distinct vertices x and y are edge …

Let R be a ring with unity. The upper ideal relation graph Γ U (R) of the ring R is the simple
undirected graph whose vertex set is the set of all non-unit elements of R and two distinct …

For a simple connected graph G of order n, the distance signless Laplacian matrix is defined
by DQ (G)= D (G)+ Tr (G), where D (G) and Tr (G) is the distance matrix and the diagonal …

For a simple graph G, the generalized adjacency matrix A α (G) is defined as A α (G)= α D
(G)+(1− α) A (G), α∈[0, 1], where A (G) is the adjacency matrix and D (G) is the diagonal …

For a finite commutative ring R with identity 1≠ 0, the weakly zero-divisor graph of R
denoted as W Γ (R) is a simple undirected graph having vertex set as a set of non-zero zero …

In this paper, we investigate the normalized distance Laplacian spectrum of the zero-divisor
graph of a commutative ring R, denoted by Γ (R), where R is taken as the ring of integers …

The comaximal graph Γ (R) of a commutative ring R is a simple graph with vertex set R and
two distinct vertices u and v of Γ (R) are adjacent if and only if u R+ v R= R. In this paper, we …

For a commutative ring R, the comaximal graph Γ (R) of R is a simple graph with vertex set R
and two distinct vertices u and v of Γ (R) are adjacent if and only if a R+ b R= R. In this …

The distance Randić matrix of a connected graph G, denoted by DR (G), was defined in Díaz
and Rojo (Bull Braz Math Soc New Ser, 2021) as follows DR (G)= T r (G)-1/2 D (G) T r (G) …

The characteristic polynomials of the Laplacian and the distance Laplacian matrices of
power graphs of groups of order pqr, where p, q and r are primes, are obtained. Further, the …