Some recent results on independence polynomials of graphs

Title: Some recent results on independence polynomials of graphs

 

SpeakerProf. Bing WeiUniversity of Mississippi

 

Date: 10:30--11:30 am, June 13, 2014

 

Place: Conference Room A404, Department of Mathematical Sciences

 

Abstract: An independent set of a graph $G$ is a set of pairwise non-adjacent vertices. Let $\alpha(G)$ denote the cardinality of a maximum independent set and $f_s(G)$ for $0\le s\le \alpha(G)$ denote the number of independent sets of $s$ vertices. The independence polynomial $I(G;x)=\sum_{i=0}^{\alpha(G)}f_s(G)x^s$ defined first by Gutman and Harary has been the focus of considerable research recently. In this talk, we will first introduce some basic concepts and tools related to the indepence polynomials of graphs, and then present some bounds for $f_s(G)$ when $G$ is a $k$-tree, a maximum $k$-degenerate graph or a compound graph. Additionally, we will characterize graphs which attain our bounds. Finally, we will propose several further research problems.

  

ContactMei Lu