学术报告(Pinkaew Siriwong 10.15)

离散数学学术报告--k-Zero-Divisor Hypergraphs

发布人:周妍 发布日期:2018-09-27
主题
离散数学学术报告--k-Zero-Divisor Hypergraphs
活动时间
-
活动地址
数学楼416讲学厅
主讲人
Pinkaew Siriwong 博士(泰国 朱拉隆功大学)

摘要:

Graph structures and algebraic structures are related; that is, a zero-divisor graph. In master thesis, we generalized the idea of a zero-divisor graph into a k-zero-divisor hypergraph including the vertex set Z(R,k), the set of all k-zero-divisors of R where k>=2. A subset {a1, a2, a3,…, ak} of Z(R, k) is an (hyper)edge if and only if (i) a1a2a3 …ak = 0 and (ii) the products of all elements of any (k 􀀀 1)-subsets of {a1, a2, a3,…, ak} are nonzero. We provided (i) a necessary condition of commutative rings that implies the completeness of their k-zero-divisor hypergraphs; (ii) a necessary condition of commutative rings that implies the ability to partition their set of all k-zero-divisors into k partite sets and the completeness of that k-partite k-zero-divisor hypergraphs; and (iii) a necessary condition of commutative rings that implies the ability to partition their set of all σ-zero-divisors into k partite sets, for some integer σ>=k. Moreover, we determined its diameter and minimum length of all cycles. Recently, we have been interested in the vertex-pursuit game played on hypergraphs.

 

数学学院

2018年9月27日