Symmetric graphs of valency seven and their basic normal quotient graphs

2019/06/24 by Pan, Jiangmin, Huang, Junjie, Wang, Chao
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.09755

Abstract

A graph Γ is basic if AutΓ has no normal subgroup N≠1 such that Γ is a normal cover of the normal quotient graph Γ_N. In this paper, we completely determine the basic normal quotient graphs of all connected 7-valent symmetric graphs of order 2pqⁿ with p < q odd primes, which consist of an infinite family of dihedrants of order 2p with p≡1(mod 7), and 6 specific graphs with order at most 310. As a consequence, it shows that, for any given positive integer n, there are only finitely many connected 2-arc-transitive 7-valent graphs of order 2pqⁿ with 7≠ p

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