图的极小循环态  

Minimal Recurrent Configuration of a Graph

作　　者：孟二霞[1] 侯耀平[1] 方爱香[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,中国长沙410081

出　　处：《湖南师范大学自然科学学报》2013年第4期26-30,共5页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(11171102)

摘　　要：图的沙堆模型是研究自组织临界现象的一个重要的模型,近年来得到广泛的应用.沙堆模型中的循环态构成了一个有限交换群.证明了沙堆模型中任一循环态总是若干个极小循环态的并,并得到了一些图运算上的极小循环态与原图的极小循环态之间的联系.The sandpile model of a graph is important to the self-organized criticality phenomenon, and has been widely applied in recent years. A finite commutative group is constituted by the recurrent configuration of a graph. It is proved that each recurrent configuration is the union of many minimal recurrent configurations. And the relationship between recurrent eordiguration and minimal recurrent configuration of the sandpile model is discussed for the operation of graphs.

关 键 词：沙堆模型 循环态 极小循环态 图的运算 

分 类 号：O157.5[理学—数学]