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.
@article{781, title = {Finite two-distance-transitive graphs of valency 6}, journal = {ARS MATHEMATICA CONTEMPORANEA}, volume = {11}, year = {2015}, doi = {10.26493/1855-3974.781.d31}, language = {EN}, url = {http://dml.mathdoc.fr/item/781} }
Jin, Wei; Tan, Li. Finite two-distance-transitive graphs of valency 6. ARS MATHEMATICA CONTEMPORANEA, Tome 11 (2015) . doi : 10.26493/1855-3974.781.d31. http://gdmltest.u-ga.fr/item/781/