Two-Distance-Transitive Graphs of Valency \(7\)

Wei Jin1, Li Tan2
1SCHOOL OF STATISTICS, JIANGXI UNIVERSITY OF FINANCE AND Eco- NOMICS, NANCHANG, JIANGXI, 330013, P.R.CHINA
2RESEARCH CENTER OF APPLIED STATISTICS, JIANGXI UNIVERSITY OF FINANCE AND ECONOMICS, NANCHANG, JIANGX!, 330013, P.R.CHINA

Abstract

A 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 \(7\).