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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...

Violations of the Ingleton inequality and revising the four-atom conjecture

Nigel Boston, Ting-Ting Nan (2020)

Kybernetika

The entropy region is a fundamental object of study in mathematics, statistics, and information theory. On the one hand, it involves pure group theory, governing inequalities satisfied by subgroup indices, whereas on the other hand, computing network coding capacities amounts to a convex optimization over this region. In the case of four random variables, the points in the region that satisfy the Ingleton inequality (corresponding to abelian groups and to linear network codes) form a well-understood...

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