题目1: Perfect Matchings in Open and Cyclic Chain Graphs

主讲人：李巍 副教授

时间：2026年09月10日（星期四）9:30

地点：理学院楼308

主办单位：理学院

主讲人简介:

李巍，西北工业大学数学与统计学院副教授、硕导，长期从事图论及其应用的研究，重点关注图的匹配理论相关问题。主持国家级项目1项、省部级项目3项。

摘要：

In this talk, we develop a unified transfer-matrix framework for counting perfect matchings in two infinite families of bounded-degree graphs built by chaining copies of a fixed base unit: the open chain and the cyclic chain.

题目2: Some works of maximal matchings in graphs

主讲人：石玲娟 副教授

时间：2026年09月10日（星期四）10:30

地点：理学院楼308

主办单位：理学院

主讲人简介:

石玲娟，西北工业大学副教授，硕士生导师。2018年毕业于兰州大学应用数学专业，获理学博士学位。主要研究领域为图论及其应用，现已在《Discrete Mathematics》、《Discrete Applied Mathematics》等国际刊物上以第一作者发表学术论文10余篇。主持国家自然科学基金委青年项目1项，主持科技部项目和陕西省项目各1项，参与国家自然科学基金委面上项目4项。

摘要：

A matching of graph G is maximal if it cannot be expanded by adding any edge to create a larger matching. Doslic et al. obtained general generating functions for the numbers of maximal matchings in three classes of benzenoid chains. By using the Hosoya vector and k-matching vector, Cruz et al. and Oz et al. researched the Hosoya index and the k-matching number of benzenoids, respectively. Inspired by these results, by using the maximal matching vector, we show that the number of maximal matchings of a benzenoid chain with n hexagons equals to the product of n certain matrices, each of which is S, L or R according to the type of the connection mode of the benzenoid chain. And by applying the perfect matching vector and maximal matching vector at a path of double hexagonal chain, we obtained the numbers of perfect matchings and maximal matchings of a double hexagonal chain with n naphthalenes. For a hexagonal ring H with n hexagons, we show that the number of maximal matchings of H equals to the trace of the product of n matrices, each of which is also S, L or R according to the type of the connection mode of H. Finally, we extend this conclusion to arbitrary polygon rings and provide an algorithm to determine the transition matrices of polygon chains (rings).