$D^L$, $D^Q$ Spectrum and Eigenvalue-free Interval of Cayley Graphs over Finite Nilpotent Groups

For a finite group $G$ and a symmetric connection set $S$, we study the distance Laplacian ($D^L$) and distance signless Laplacian ($D^Q$) spectrum of the Cayley graph $\Cay(G,S)$ for $G$ a finite nilpotent group. Using the internal direct product decomposition over Sylow subgroups, we reduce every