Given a commutative ring R with identity 1≠ 0, let the set Z (R) denote the set of zero-
divisors and let Z*(R)= Z (R)\{0} be the set of non-zero zero-divisors of R. The zero-divisor …

A topological index is a number generated from a molecular structure (ie, a graph) that
indicates the essential structural properties of the proposed molecule. Indeed, it is an …

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, the power graph P (G) is a simple connected graph whose vertex set is
the set of elements of G and two distinct vertices x and y are adjacent if and only if xi= y or …

For a finite commutative ring Zn with identity 1= 0, the zero divisor graph Γ (Zn) is a simple
connected graph having vertex set as the set of non-zero zero divisors, where two vertices x …

Let G be a simple, connected graph of order n. Its distance Laplacian energy DLE (G) is
given by DLE (G)=∑ i= 1 n| ρ i L− 2 W (G) n|, where ρ 1 L≥ ρ 2 L≥⋯≥ ρ n L are the …

Let R be a finite commutative ring with non zero identity. The unit graph of R denoted by G
(R) is the graph obtained by setting all the elements of R to be the vertices of a graph and …

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

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 distance matrix D of a connected graph G is the matrix indexed by the vertices of G
where Di, j= d (vi, vj) and d (vi, vj) denotes the distance between the vertices vi and vj. The …