On the structure of the Jacobian group for circulant graphs
On the structure of the Jacobian group for circulant graphs
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循环图雅可比群的结构
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
I. Mednykh
中科院分区：
文献类型：
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作者：
A. Mednykh;I. Mednykh
图的雅可比行列式被定义为由遵守两个基尔霍夫定律的流生成的最大阿贝尔群。这一概念也称为皮卡德群、沙堆群或临界群，在过去十年中已被许多作者广泛研究。这是有限图的一个重要的代数不变量。同时，雅可比行列式的结构仅在特定情况下才为人所知。本文致力于循环图雅可比群结构的研究。对于该族中最简单的图，明确描述了雅可比群，并且在一般情况下，提出了计算它的有效算法。
The Jacobian of a graph is defined as the maximal Abelian group generated by flows obeying two Kirchhoff’s laws. This notion, also known as the Picard group, sandpile group, or critical group, has been extensively studied by many authors in the past decade. This is an important algebraic invariant of a finite graph. At the same time, the structure of the Jacobian is known only in particular cases. The paper is devoted to the study of the structure of the Jacobian group for circulant graphs. For the simplest graphs in this family, the Jacobian group is explicitly described, and in the general case, and effective algorithm for calculating it is proposed.