Cubic girth-regular graphs of even girth
Ponente: Štefánia Glevitzká
Institución: Comenius University
Tipo de Evento: Investigación
Institución: Comenius University
Tipo de Evento: Investigación
| Cuándo |
05/11/2025 de 16:00 a 17:00 |
|---|---|
| Dónde | ZOOM ID 675 648 7475, código de acceso: V2hgZi!! |
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For a graph G of finite girth, each vertex v of G can be associated with a list of integers, one integer per each edge incident with v representing the number of girth cycles containing the edge (which may possibly be 0). If each of the lists associated with the vertices of G is the same (and so, in particular, 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.
The concept of girth-regularity was introduced by Potočnik and Vidali in 2019, who also proved multiple necessary conditions on signatures, classified cubic girth-regular graphs of girth at most 5 as well as cubic vertex-transitive graphs of girth 6. In our work, we extend the latter to a classification of all cubic girth-regular graphs of girth 6 and present some additional conditions on signatures of cubic girth-regular graphs of even girth.
