Some integer values in the spectra of burnt pancake 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 $\{0,1,\dots ,n\}\setminus \{\lfloor n/2\rfloor \}$.

Fixed typos and other small changes. Final version to appear in Linear Algebra and its Applications