Geodesic
Finite two-distance-transitive graphs of valency 6
Ars Mathematica Contemporanea, Tome 11 (2016) no. 1, pp. 49-58.

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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.
DOI : 10.26493/1855-3974.781.d31
Keywords: 2-Distance-transitive graph, 2-arc-transitive graph, permutation group. 
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Wei Jin; Li Tan. Finite two-distance-transitive graphs of valency 6. Ars Mathematica Contemporanea, Tome 11 (2016) no. 1, pp. 49-58. doi : 10.26493/1855-3974.781.d31. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.781.d31/

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