A class of integral graphs constructed from the hypercube

TL;DR

This paper investigates the spectral properties of a specific class of integral graphs derived from the hypercube, revealing they have exactly five integer eigenvalues, which enhances understanding of hypercube-induced graphs.

Contribution

It explicitly determines the eigenvalues of line graphs from the first and second layers of hypercubes, showing they are all integers with exactly five distinct values.

Findings

The line graph has exactly five distinct eigenvalues.

All eigenvalues of these graphs are integers.

The eigenvalues are explicitly characterized.

Abstract

In this paper, we determine the set of all distinct eigenvalues of the line graph which is induced by the first and second layers of the hypercube $ Q_n $, $n>3$. We show that this graph has precisely five distinct eigenvalues and all of its eigenvalues are integers