Some bounds on the distance-sum-connectivity matrix

Abstract

The distance-sum-connectivity matrix of a graph G is expressed by $\delta \left(i\right)$ and $\delta \left(j\right)$ such that $i,j\in V$ . $\delta \left(i\right)$ and $\delta \left(j\right)$ are represented by a sum of the distance matrices for $i<v$ and $j<v$ , respectively. The purpose of this paper is to give new inequalities involving the eigenvalues, the graph energy, the graph incidence energy, and the matching energy. So, we have some results in terms of the edges, the vertices, and the degrees.

Keywords: Bounds; Distance-sum-connectivity matrix.