Proceedings of the International Conference on Geometry, Integrability and Quantization

On the Jacobian Group for Möbius Ladder and Prism Graphs

Madina Deryagina and Ilia Mednykh

Abstract

The notion of the Jacobian group of graph (also known as Picard 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 of the Jacobian group coincides with the number of spanning trees for a graph. The latter number is known for the simplest families of graphs such as Wheel, Fan, Prism, Ladder and Möbius ladder graphs. At the same time the structure of the Jacobian group is known only in several cases. The aim of this paper is to determine the structure of the Jacobian group of the Möbius ladder and Prism graphs.

Article information

Source
Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Andrei Ludu and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2014), 117-126

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815705

Digital Object Identifier
doi:10.7546/giq-15-2014-117-126

Mathematical Reviews number (MathSciNet)
MR3287752

Zentralblatt MATH identifier
1314.05094

Citation

Deryagina, Madina; Mednykh, Ilia. On the Jacobian Group for Möbius Ladder and Prism Graphs. Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, 117--126, Avangard Prima, Sofia, Bulgaria, 2014. doi:10.7546/giq-15-2014-117-126. https://projecteuclid.org/euclid.pgiq/1436815705


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