Seminár z teórie grafov - Štefánia Glevitzká (2.10.2025)
vo štvrtok 2.10.2025 o 9:50 hod. v miestnosti M 213
Prednášajúca: Štefánia Glevitzká
Názov prednášky: Cubic girth-regular graphs of even girth
Termín: 2.10.2025, 9:50 hod., M 213
Abstrakt:
For a graph G of finite girth, each vertex v of G can be associated with a list of integers, one integer for each edge incident with v, representing the number of girth cycles containing the edge (possibly 0). If the lists associated with the vertices of G are all identical (and so G is regular), we say that G is girth-regular, and the shared list is said to be the signature of G. Note that all vertex-transitive graphs are necessarily girth-regular. Recently, research in this area focuses on classifying girth-regular or vertex-transitive graphs of small girth and degree (mostly cubic). In this talk, we recall a characterization of cubic girth regular graphs of girth 6. Inspired by that, we present multiple necessary conditions on signatures of cubic girth-regular graphs of any even girth and discuss some areas of further improvement.