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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...

Weakly-exceptional quotient singularities

Dmitrijs Sakovics (2012)

Open Mathematics

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D n, E 6, E 7, E 8. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.

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