Student Seminar
Speaker: Garima Khetawat, IIT Bombay
Host: Santanu Dey
Title: Independence attractors of graphs
Time, day and date: 2:00:00 PM – 2:45:00 PM, Thursday, October 09
Venue: Room 113
Abstract: By an independent set in a simple graph G, we mean a set of pairwise non-adjacent vertices in G. The independence polynomial of G is defined as IG(z) = a0+a1z+a2z 2+ · · · + aβz β , where ai is the number of independent sets in G with cardinality i and β denotes the cardinality of a largest independent set in G, known as the independence number of G. Let Gm denote the m-times lexicographic product of G with itself. The independence attractor of G, denoted by A (G), is defined as A (G) = limm→∞{z : IGm(z) = 0}, where the limit is taken with respect to the Hausdorff metric on the space of all compact subsets of the plane. In this talk, we discuss some results (without proofs) regarding the possibility of independence attractors being circles or line segments.