报告题目：Total domination polynomials of graphs

报告摘要：Given a graph $G$,  a total dominating set $D_t$ of $G$ is a vertex set that every vertex of $G$  is adjacent to at least one vertex of $D_t$. Let $d_t(G,i)$ be  the number of all total dominating sets of $G$ with size $i$. The total domination polynomial of $G$ is $D_t(G,x)=\sum\limits_{i=1}^{| V(G)|} d_t(G,i)x^i$. In this paper, we obtain the vertex-reduction and edge-reduction formulas for 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. Finally, we use the reduction-formulas to investigate  the relations between vertex set of degree 2 and  coefficients of total domination polynomials in $G$.

报告人：王绍辉，博士，Savannah State University助理教授，2012年于华中师范大学获得数学硕士，2016年于美国密西西比大学获得数学博士学位。研究领域为图论和代数组合。在Applied Mathematical Modelling，Discrete Applied Mathematics，Applied Mathematics and Computation,  Journal of Mathematical Analysis and Applications等国际权威学术期刊发表论文20多篇。

报告时间：2018年6月20号（周三）上午10:00-11:00
报告地点：长清校区B434报告厅

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