On (distance) Laplacian characteristic polynomials of power graphs

Abstract

The characteristic polynomials of the Laplacian and the distance Laplacian matrices of power graphs of groups of order $pqr$, where $p,q$ and $r$ are { primes,} are obtained. Further, the characteristic polynomials of these matrices for proper power graphs of cyclic and dicyclic groups are given. The important inequalities for the zeros of the distance Laplacian characteristic polynomials of power graphs of finite groups are presented in comments.

19 pages, 1 figure