Maruša Lekše: Cubic vertex-transitive graphs of girth 7

Cubic vertex-transitive graphs of girth 7

Maruša Lekše

Abstract: Let Γ be a graph, and let v and e be a vertex and an edge of Γ. The signature of e is the number of girth cycles that contain it, while the signature of v is the tuple of the signatures of all of the edges incident to it (ordered by size). We say that Γ is girth-regular if all vertices in the graph have the same signature. Potočnik and Vidali introduced this concept in 2019 as a generalization of edge-girth-regularity and later used it to classify cubic vertex-transitive graphs of girth at most 6. In this talk we will present a similar classification of cubic vertex-transitive graphs of girth 7 based on their signature, and some corollaries of this classification.