Some integer values in the spectra of burnt pancake graphs

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