  The spined cube $SQ_n$ is a variant of the hypercube $Q_n$, introduced by
Zhou et al. in [Information Processing Letters 111 (2011) 561-567] as an
interconnection network for parallel computing. A graph $\G$ is an $m$-Cayley
graph if its automorphism group $\Aut(\G)$ has a semiregular subgroup acting on
the vertex set with $m$ orbits, and is a Caley graph if it is a 1-Cayley graph.
It is well-known that $Q_n$ is a Cayley graph of an elementary abelian 2-group
$\mz_2^n$ of order $2^n$. In this paper, we prove that $SQ_n$ is a 4-Cayley
graph of $\mz_2^{n-2}$ when $n\geq6$, and is a $\lfloor n/2\rfloor$-Cayley
graph when $n\leq 5$. This symmetric property shows that an $n$-dimensional
spined cube with $n\geq6$ can be decomposed to eight vertex-disjoint
$(n-3)$-dimensional hypercubes, and as an application, it is proved that there
exist two edge-disjoint Hamiltonian cycles in $SQ_n$ when $n\geq4$. Moreover,
we determine the vertex-transitivity of $SQ_n$, and prove that $SQ_n$ is not
vertex-transitive unless $n\leq3$.
