On the Critical Group of Graph S_m·C_n
WU Hai-yan · Journal of Zhuzhou Teachers College · 2006
The critical group of a connected graph is a finite abelian group whose structure is a subtle isomorphism invariant of the graph.It is closely connected with the graphic Laplacian theory.This paper studied the structure of the critical group on the graph S_m·C_n,gave an explicit expression of the Smith normal form of critical group on it,and demonstrated that the critical group on the graph S_m·C_n is isomorphic to Z~((m-2)n+2)_(2)Z~(n-2)_(2m)Z_(2mn).