Tian and Meng in [Y. Tian and J. Meng, c  -Optimally half vertex transitive graphs with regularity , Information Processing Letters 109 (2009) 683-686] shown that a connected half vertex transitive graph with regularity and girth is cyclically optimal. In this paper, we show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree k k   6 g G   ...

In this paper, we prove that every vertex-transitive graph can be expressed as the edge-disjoint union of symmetric graphs. We define a multicycle graph and conjecture that every vertex-transitive graph cam be expressed as the edge-disjoint union of multicycles. We verify this conjecture for several subclasses of vertextransitive graphs, including Cayley graphs, multidimensional circulants, and...

A nonidentity element of a permutation group is said to be semiregular if all of its orbits have the same length. The work in this paper is linked to [6] where the problem of existence of semiregular automorphisms in vertex-transitive digraphs was posed. It was observed there that every vertex-transitive digraph of order pk or mp, where p is a prime, k 1 and m p are positive integers, has a sem...

A 1 2 -arc-transitive graph is a vertexand edgebut not arc-transitive graph. In all known constructions of quartic 1 2 -arc-transitive graphs, vertex stabilizers are isomorphic to Z 2,Z 2 2 or to D8. In this article, for each positive integer m ≥ 1, an infinite family of quartic 1 2 -arctransitive graphs having vertex stabilizers isomorphic to Z m

Let $G$ be a permutation group on set $\Omega$ and recall that base for is subset of such its pointwise stabiliser trivial. In recent paper, Burness Giudici introduced the Saxl graph $G$, denoted $\Sigma(G)$, with vertex two vertices adjacent if they form base. If transitive, then $\Sigma(G)$ vertex-transitive it natural to consider valency (which we refer as $G$). this paper present general me...