### Finite two-distance-transitive graphs of valency 6

#### Abstract

A non-complete graph Gamma is said to be (G,2)-distance-transitive if, for i = 1,2 and for any two vertex pairs (u_1,v_1) and (u_2,v_2) with d_Gamma(u_1,v_1) = d_Gamma(u_2,v_2) = i, there exists g in G such that (u_1,v_1)^g=(u_2,v_2). This paper classifies the family of (G,2)-distance-transitive graphs of valency 6 which are not (G,2)-arc-transitive.

#### Keywords

2-Distance-transitive graph, 2-arc-transitive graph, permutation group.

DOI: https://doi.org/10.26493/1855-3974.781.d31

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications