Distance spectra of some double join of graphs and some new families of distance equienergetic graphs

TL;DR

This paper calculates the distance spectra of certain double join graphs and introduces new families of graphs that are distance equienergetic with diameter 3, expanding understanding of graph spectral properties.

Contribution

It provides explicit spectral calculations for double join graphs and constructs new distance equienergetic graph families with diameter 3.

Findings

Spectra of specific block matrices computed

Distance spectra of double join graphs characterized

New families of distance equienergetic graphs identified

Abstract

In this paper we compute the spectrum of a special block matrix and use it to describe the distance spectra of some double join of graphs. As an application, we give several families of distance equienergetic graphs of diameter 3.