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理学院2017-2018学年夏季第二周学术报告(三)

发布时间:2018-07-05

学 术 报 告

 

报告题目: Total domination number and polynomials of graphs

 

报告学者:卫兵 教授

 

报告者单位University of Mississppi

 

报告时间2016年7月19日下午4:00-5:00      

 

报告地点学活1005

 

摘要: Given a graph $G$, a total dominating set $D_t$  is a vertex set that every vertex of $G$  is adjacent to some vertices of $D_t$ and let $d_t(G,i)$ be  the number of all total dominating sets with size $i$. The total domination number, denoted by $\gamma_t(G)$, is the cardinality of a smallest total dominating set and  the total domination polynomial is defined as $D_t(G,x)=\sum\limits_{i=1}^{| V(G)|} d_t(G,i)x^i$. Finding upper and lower bounds for total domination number and studying the properties of graph polynomials are hot and important topics in graph theory. In this talk, we will introduce some bounds for $\gamma_t(G)$ and provide the vertex-reduction and edge-reduction formulas of total domination polynomials. As  consequences, we give the total domination polynomials for paths and cycles. Additionally, we determine the sharp upper bounds of total domination polynomials for trees and  characterize the corresponding graphs attaining such bounds. Further research problems related to $\gamma_t(G)$ and $D_t(G,x)$ will be proposed.

 

主办教师:郝荣霞

欢迎广大同学老师积极踊跃参加!