ON THE STRUCTURE OF PICARD GROUP FOR MOEBIUS LADDER GRAPH AND PRISM GRAPH
Abstract
The notion of the Picard group of graph (also known as Jacobian group, sandpile group, critical group) was independently given by many authors. This is a very important algebraic invariant of a finite graph. In particular, the order ofthe Picard group coincides with the number ofspanning trees for a graph. The latter number is known for the simplest families of graphs such as Wheel, Fan, Prism, Ladder and Moebius ladder graphs. At the same time the structure of the Picard group is known only in several cases. The aim of this paper is to determine the structure of the Picard group of the Moebius ladder and Prism graphs.
About the Authors
Madina Alexandrovna Zindinova
Novosibirsk State University
Russian Federation
Russian Federation
Ilia Aleksandrovich Mednykh
Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
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Review
For citations:
Zindinova M.A., Mednykh I.A. ON THE STRUCTURE OF PICARD GROUP FOR MOEBIUS LADDER GRAPH AND PRISM GRAPH. The Bulletin of Kemerovo State University. 2011;(3-1):50-57. (In Russ.)
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