Pentavalent symmetric graphs of order 2pq

Arc-transitive Pentavalent Graphs of Order 4pq

This paper determines all arc-transitive pentavalent graphs of order 4pq, where q > p > 5 are primes. The cases p = 1, 2, 3 and p = q is a prime have been treated previously by Hua et al. [Pentavalent symmetric graphs of order 2pq, Discrete Math. 311 (2011), 2259-2267], Hua and Feng [Pentavalent symmetric graphs of order 8p, J. Beijing Jiaotong University 35 (2011), 132-135], Guo et al. [Pentav...

Classifying pentavalnet symmetric graphs of order $24p$

A graph is said to be symmetric if its automorphism group is transitive on its arcs. A complete classification is given of pentavalent symmetric graphs of order 24p for each prime p. It is shown that a connected pentavalent symmetric graph of order 24p exists if and only if p=2, 3, 5, 11 or 17, and up to isomorphism, there are only eleven such graphs.

Pentavalent symmetric graphs of order twice a prime power

Non-Cayley Vertex-Transitive Graphs of Order Twice the Product of Two Odd Primes

For a positive integer n, does there exist a vertex-transitive graph r on n vertices which is not a Cayley graph, or, equivalently, a graph r on n vertices such that Aut F is transitive on vertices but none of its subgroups are regular on vertices? Previous work (by Alspach and Parsons, Frucht, Graver and Watkins, MaruSic and Scapellato, and McKay and the second author) has produced answers to ...

Cubic symmetric graphs of orders $36p$ and $36p^{2}$

A graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. In this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.