TY - JOUR
T1 - On the critical group of the Möbius ladder graph
AU - Chen, Pingge
AU - Hou, Yaoping
AU - Woo, Chingwah
PY - 2006
Y1 - 2006
N2 - The critical group of a connected graph is a finite abelian group whose order is the number of spanning trees and whose structure is a subtle isomorphism invariant of the graph. In this paper we study the structure of the critical group on the Möbius ladder, and we prove that the Smith normal form of the critical group is not cyclic but is always the direct sum of two or three cyclic groups.
AB - The critical group of a connected graph is a finite abelian group whose order is the number of spanning trees and whose structure is a subtle isomorphism invariant of the graph. In this paper we study the structure of the critical group on the Möbius ladder, and we prove that the Smith normal form of the critical group is not cyclic but is always the direct sum of two or three cyclic groups.
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M3 - RGC 21 - Publication in refereed journal
SN - 1034-4942
VL - 36
SP - 133
EP - 142
JO - Australasian Journal of Combinatorics
JF - Australasian Journal of Combinatorics
ER -