On Distance Spectral Radius and Distance Energy of Graphs

TL;DR

This paper investigates bounds for the distance spectral radius and distance energy of graphs, providing new theoretical limits and characterizations of extremal graphs in spectral graph theory.

Contribution

It establishes new lower and upper bounds for the distance spectral radius and energy, and characterizes extremal graphs for these spectral parameters.

Findings

Derived lower bounds for the distance spectral radius of graphs and bipartite graphs.

Established lower bounds for the distance energy of graphs.

Discussed upper bounds for the distance energy.

Abstract

For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix, and the distance energy is defined as the sum of the absolute values of the eigenvalues of its distance matrix. We establish lower and upper bounds for the distance spectral radius of graphs and bipartite graphs, lower bounds for the distance energy of graphs, and characterize the extremal graphs. We also discuss upper bounds for the distance energy.