报告题目：Properties on algebra structure graphs

报告人：边红 教授，新疆师范大学

报告地点：五教5101

报告时间：10月12日 上午8：40-9：20

摘要：

In order to study the structure and properties of a group by using graphs, there are two main methods to define graphs through these groups. One is to define through the elements of a group, such as directed power graphs, undirected power graphs, enhanced power graphs, commuting graphs, non-commuting graphs, prime graphs, and generating graphs, non-generating graphs. Another is to define a graph through the subgroups of a group, such as inclusion graphs of subgroups, intersection graphs, and co-maximal subgroup graphs. For a finite group G, the co-maximal subgroup graph of G, denoted by Γ (G), is a graph whose vertices are proper subgroups of G, and two distinct vertices H and K are adjacent if and only if HK = G. The deleted co-maximal subgroup graph? ∗ (G) is obtained by removing isolated vertices from Γ(G). In this paper, we first present some new properties of ? ∗ (G) for a finite group G. Moreover, according to the structure theorem of finite Abelian group, we give the formula of the sandpile group of polygon flower with two centers. As application of our results, we present the sandpile group of hexagonal chain, and sandpile groups of catacondensed system with two branched hexagons.