This week's seminar is given by our own Dmitrii Panasenko, Umeå universitet.
Title: Strictly Deza graphs and the vertex connectivity
Abstract: A k-regular graph on v vertices is called a Deza graph with parameters (v, k, b, a), b ≥ a if the number of common neighbors of any two distinct vertices takes two values: a or b. A Deza graph is called a strictly Deza graph if it has diameter 2 and is not strongly regular.
In this talk we will discuss the enumeration of strictly Deza graphs and the enumeration of special subclass of strictly Deza graphs called divisible design graphs. We will also discuss the constructions of divisible design graphs found during the enumeration.
We will also discuss the vertex connectivity of strictly Deza graphs and divisible design graphs. We will talk about cases with vertex connectivity less than k, where k is the regularity of the graph. In particular, we will show that the vertex connectivity of strictly Deza graphs can be less than k by any amount.
