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Valency seven symmetric graphs of order 2 p q

Xiao-Hui Hua, Li Chen (2018)

Czechoslovak Mathematical Journal

A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, all connected valency seven symmetric graphs of order 2 p q are classified, where p , q are distinct primes. It follows from the classification that there is a unique connected valency seven symmetric graph of order 4 p , and that for odd primes p and q , there is an infinite family of connected valency seven one-regular graphs of order 2 p q with solvable automorphism groups, and there are four sporadic ones...

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