Some integer values in the spectra of burnt pancake graphs

TL;DR

This paper investigates the spectral properties of burnt pancake graphs, revealing that their adjacency spectra include all integers from 0 to n except the floor of n/2, highlighting specific spectral characteristics.

Contribution

The paper proves that the adjacency spectrum of burnt pancake graphs contains all integers from 0 to n except one specific value, providing new insights into their spectral structure.

Findings

Spectral analysis of $ ext{BP}_n$ includes all integers 0 to n except $loor{n/2}$.

Identifies specific integer values in the spectrum of burnt pancake graphs.

Advances understanding of spectral properties of permutation-based graphs.

Abstract

The burnt pancake graph, denoted by $\mathbb{BP}_n$, is formed by connecting signed permutations via prefix reversals. Here, we discuss some spectral properties of $\mathbb{BP}_n$. More precisely, we prove that the adjacency spectrum of $\mathbb{BP}_n$ contains all integer values in the set $\{0, 1, \ldots, n\}\setminus\{\left\lfloor n/2 \right\rfloor\}$.