Finite two-distance-transitive graphs of valency 6 - Jin, Wei (Ars mathematica contemporanea, 2016)
A non-complete graph ?$Γ$? 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 ?$d_{Γ}(u_1,v_1) = d_{Γ}(u_2,v_2) = i$?, 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-ločnotranzitiven graf; 2-razdaljno-tranzitiven graf; permutacijska grupa