Algebraic Graph Theory Seminar - István Porupsánszki (22.3.2024)

Friday 22.3.2024 at 13:00, Lecture room M/IX (online too)

19. 03. 2024 16.31 hod.
By: Martin Mačaj

István Porupsánszki (Eotvos Lorand University, Budapest):
Extremal edge-girth-regular graphs

Termín: 22.3.2024, 13:00 hod., M IX a MS Teams

Abstract:
In my talk, I will introduce the edge-girth-regular cage problem which is the generalization of the cage problem. A graph of order n is called edge-girth-regular if it is a k-regular graph of girth g such that every edge is contained in exactly λ distinct girth cycles. We denote such a graph with egr(n,k,g,λ). The edge-girth-regular cage problem consists in finding an egr(n,k,g,λ) where the triple (k,g,λ) is fixed and the order n is minimal. There are two main parts of the problem: we need constructions and then we need tools to check whether they are extremal. I will talk about three lower bounds on the order of extremal egr graphs.them are combinatorial and the third one is purely algebraic. Its proof is based on the properties of the eigenvalues of the adjacency matrix.

Those of you who are not able to attend in person or who are still uncertain about the safety of attending in person are welcome to attend via MS Teams. In either case, we hope to see as many of you as possible (either in person or virtually) at our Friday gatherings.