Speaker: Karen Collins, Wesleyan University

Date and Time: Wednesday, November 4, 3.40pm Atlantic time. Zoom link below.

Title: Split graphs and their degree sequences

Abstract: A graph is a set of vertices and a set of pairs of vertices, called edges. The degree of a vertex is the number of edges that contain it.  Some information about a graph arises from its sequence of vertex degrees, and there is a numerical way to recognize which sequences of positive integers are the sequences of vertex degrees of a graph. A graph is a split graph if its vertex set can be partitioned into a clique and an independent (or stable) set. A split graph can model a social network consisting of 2 groups of people, so that all pairs of people from the clique are friends, and no pair of people from the stable set are friends. Given only the degree sequence of a graph, there is a way to recognize whether or not the graph is a split graph. In this talk, we will explore a geometric representation of the degree sequence of a graph, with special attention to degree sequences of split graphs. 

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