Abstract A graph $\Gamma $ is called $(G, s)$ -arc-transitive if $G \le \text{Aut} (\Gamma )$ transitive on the set of vertices and s -arcs , where for an integer $s \ge 1$ -arc a sequence $s+1$ $(v_0,v_1,\ldots ,v_s)$ such that $v_{i-1}$ $v_i$ are adjacent $1 i s$ $v_{i-1}\ne v_{i+1}$ s-1$ . 2-transitive it $(\text{Aut} ), 2)$ but not 3)$ -arc-transitive. Cayley group G normal in $\text{Aut} n...

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...