For a graph G with V (G)={v1, v2,..., vn} and degree sequence (dv1, dv2,..., dvn), the
adjacency matrix A (G) of G is a (0, 1) square matrix of order n with ij-th entry 1, if vi is …

For a positive real number k, the k-Sombor index of a graph G, introduced by Réti et al, is
defined as SO k (G)=∑ uv∈ E (G) d (u) k+ d (v) kk, where d (u) denotes the degree of the …

In this article, we are interested in characterizing graphs with three distinct arithmetic–
geometric eigenvalues. We provide the bounds on the arithmetic–geometric energy of …

Let G be a simple graph with the vertex set V={v 1,…, vn} and denote by dvi the degree of
the vertex vi. The modified Sombor index of G is the addition of the numbers (dvi 2+ dvj 2) …

The Sombor index has gained lot of attention in the recent days for its mathematical
properties and chemical applicabilities. Here, we initiated the novel block number version of …

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 …

We study the Sombor index and the Sombor spectral properties of chain graphs. In
particular, an explicit formula for the Sombor index is given, the Sombor eigenvalues are …

In a graph G, if di is the degree of a vertex vi, the geometric-arithmetic matrix GA (G) is a
square matrix whose (i, j)-th entry is 2 didjdi+ dj whenever vertices i and j are adjacent and 0 …

For a simple graph G with vertex set {v 1,⋯, vn} and degree sequence {d 1,⋯, dn}, the
Sombor matrix S (G) of G is an n× n matrix, whose (i, j)-th entry is di 2+ dj 2, if vi and vj are …

For a simple graph with vertex set {v 1, v 2,…, vn} and degree sequence dvii= 1, 2,…, n, the
inverse sum indeg matrix (ISI matrix) A ISI (G)=(aij) of G is a square matrix of order n, where …