The Distance Energy of Clique Trees

TL;DR

This paper investigates the distance energy of clique trees, providing a positive resolution to a conjecture about their spectral properties, thereby advancing understanding of graph energy in spectral graph theory.

Contribution

It offers a proof confirming a conjecture on the distance energy of clique trees, contributing new insights into their spectral characteristics.

Findings

Confirmed the conjecture on the distance energy of clique trees.

Established properties of the distance eigenvalues for clique trees.

Enhanced understanding of spectral graph theory related to graph energy.

Abstract

The distance energy of a simple connected graph $G$ is defined as the sum of absolute values of its distance eigenvalues. In this paper, we mainly give a positive answer to a conjecture of distance energy of clique trees proposed by Lin, Liu and Lu [H.~Q.~ Lin, R.~F.~Liu, X.~W.~Lu, The inertia and energy of the distance matrix of a connected graph, {\it Linear Algebra Appl.,} 467 (2015), 29-39.]