Classifying cubic s-regular graphs of orders 22p and 22p²

A graph is s-regular if its automorphism group acts regularly on the set of s-arcs. In this study, we classify the connected cubic s-regular graphs of orders 22p and 22p² for each s ≥ 1, and each prime p

Edge-transitive regular Zn-covers of the Heawood graph

AbstractA regular cover of a graph is said to be an edge-transitive cover if the fibre-preserving automorphism subgroup acts edge-transitively on the covering graph. In this paper we classify edge-transitive regular Zn-covers of the Heawood graph, and obtain a new infinite family of one-regular cubic graphs. Also, as an application of the classification of edge-transitive regular Zn-covers of the Heawood graph, we prove that any bipartite edge-transitive cubic graph of order 14p is isomorphic to a normal Cayley graph of dihedral group if the prime p>13

On application of linear algebra in classification cubic s-regular graphs of order 28p

A graph is s-regular if its automorphism group acts regularly on the set of s-arcs. In this paper, by applying concept linear algebra, we classify the connected cubic s-regular graphs of order 28p for each s ≥ 1, and prime p

Cubic symmetric graphs of order a small number times a prime or a prime square

AbstractA graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular elementary abelian coverings of the complete bipartite graph K3,3 and the s-regular cyclic or elementary abelian coverings of the complete graph K4 for each s⩾1 are classified when the fibre-preserving automorphism groups act arc-transitively. A new infinite family of cubic 1-regular graphs with girth 12 is found, in which the smallest one has order 2058. As an interesting application, a complete list of pairwise non-isomorphic s-regular cubic graphs of order 4p, 6p, 4p2 or 6p2 is given for each s⩾1 and each prime p