The Critical Group of the Corona of Trees and Cycles

Abstract

The critical group of a connected graph is a refinement of the number of spanning trees of the graph. It is a subtle isomorphism invariant of the graph and is closely connected with the graph Laplacian matrix. In this paper, the structure of the critical group of the corona of trees and cycles is determined and the explicit expression of the Smith normal form of critical group on the corona of trees and circle are given.