Doctoral colloquium - Dominika Závacká (28.10.2024)
Monday 4.11.2024 at 13:10, Lecture room I/9
Dominika Závacká:
Algorithmic approach to obtaining values of (k,g)-spectrum*
Abstract:
A (k,g)-graph is defined as a k-regular graph with a girth of g. A (k,g)-spectrum denotes the set of all possible orders of (k,g)-graphs. The smallest order in the (k,g)-spectrum corresponds to the (k,g)-cage, which is the smallest known (k,g)-graph. We will present various methods for identifying possible orders within the (k,g)-spectrum. As determining the smallest value of (k, g)-spectrum is a hard problem, we focus on cases where the minimal order (the order of the (k,g)-cage) is already established. Given the challenges of establishing the full (k,g)-spectrum, we provide both complete and partial computations for several pairs of (k,g).
(joint work with: Leonard Chidiebere Eze, Róbert Jajcay, Tatiana Jajcayová)