Title: Deza graphs and vertex connectivity
| Speaker: | Dmitriy Panasenko |
| Affiliation: | Umeå University |
| Location: | Please contact Sabrina Lato for Zoom link. |
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 describe the constructions of divisible design graphs found during the enumeration.
In the second part of talk we discuss the vertex connectivity of strictly Deza graphs and divisible design graphs. We will look at the 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.