2025/08/27 by Lekše, Maruša, Toledo, Micael
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.19880
In this paper we classify cubic vertex-transitive graphs of girth 7, based on their signature. Such a graph is either a truncation of an arc-transitive dihedral scheme on a 7-regular graph, the skeleton of a rotary map of type \7,3\, a member of an infinite family of Cayley graphs, or is one of the of the generalised Petersen graphs Pet(13,5), Pet(15,4), Pet(17,4) or the Coxeter graph. We show that for a cubic vertex-transitive graphs Γ of girth 7, if every edge of Γ is contained in the same number of 7-cycles, then Γ is also arc-transitive.