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- W4288314334 abstract "A graph $Gamma$ is basic if Aut$Gamma$ has no normal subgroup $Nne1$ such that $Gamma$ is a normal cover of the normal quotient graph $Gamma_N$. In this paper, we completely determine the basic normal quotient graphs of all connected 7-valent symmetric graphs of order $2pq^n$ with $p < q$ odd primes, which consist of an infinite family of dihedrants of order $2p$ with $pequiv1$(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 $2pq^n$ with $7ne p<q$ primes, partially generalizing Theorem 1 of Conder, Li and Potocnik [On the orders of arc-transitive graphs, J. Algebra 421 (2015), 167-186]." @default.
- W4288314334 created "2022-07-28" @default.
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- W4288314334 date "2019-06-24" @default.
- W4288314334 modified "2023-09-30" @default.
- W4288314334 title "Symmetric graphs of valency seven and their basic normal quotient graphs" @default.
- W4288314334 doi "https://doi.org/10.48550/arxiv.1906.09755" @default.
- W4288314334 hasPublicationYear "2019" @default.
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