Suppose G is a finite group. The power graph represented by P (G) of G is a graph, whose
node set is G, and two different elements are adjacent if and only if one is an integral power …

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 …

For a simple connected graph G of order n, the normalized Laplacian is a square matrix of
order n, defined as ℒ (G)= D (G)−<? A3B2 [thinspace]?> 1 2 L (G) D (G)−<? A3B2 …

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 …

The normalized distance Laplacian matrix of a connected graph G, denoted by D 𝓛 (G), is
defined by D 𝓛 (G)= Tr (G)− 1/2 DL (G) Tr (G)− 1/2, where D (G) is the distance matrix, the DL …

Let G be a connected graph of order n. Let Diag (Tr) be the diagonal matrix of vertex
transmissions and let D (G) be the distance matrix of G. The distance signless Laplacian …

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 …

For a finite group 𝒢, the power graph 𝒫 (𝒢) is a connected simple graph, whose vertex set is
the set of elements of 𝒢 and two vertices are connected by an edge if and only if one is the …

Let G be a connected graph with n vertices, m edges. The distance signless Laplacian
matrix DQ (G) is defined as DQ (G)= Diag (Tr (G))+ D (G), where Diag (Tr (G)) is the diagonal …