Some integer values in the spectra of burnt pancake graphs

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