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Tuesday, December 6 • 8:40am - 9:00am
A Survey Of Results Concerning Properties Of Independence Polynomials

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We present a survey of approaches concerning the independence polynomial of a variety of graphs. A graph G is a collection of vertices V and edges E, which may be represented as points in space and line segments connecting these points.The independence polynomial relays important combinatorial information concerning the graph. We consider various properties such a polynomial may or may not have including symmetry, unimodality and log-concavity. Specifically we focus on almost 3-regular trees and a path like tree whose independence polynomials can be computed with recurrence relations. We work on measuring the log-concavity and unimodality of these polynomials. Also, given certain conditions on two arbitrary log-concave polynomials we determine that their sum can be at worst bimodal.

Tuesday December 6, 2016 8:40am - 9:00am PST
202 Zeis Hall