The Laplacian spectrum of power graphs of cyclic and dicyclic groups

Ramesh Prasad Panda

Published 2017-06-08Version 1

The power graph of a group $G$ is the graph whose vertex set is $G$ and two distinct vertices are adjacent if one is a power of the other. In this paper, certain upper and lower bounds of algebraic connectivity of power graphs of finite cyclic groups are given. Then the Laplacian spectrum of power graphs of dicyclic groups is discussed and the complete Laplacian spectrum of power graphs of generalized quaternion groups (dicyclic $2$-groups) is computed.