\input zb-basic
\input zb-ioport
\iteman{io-port 05377321}
\itemau{Choudum, S.A.; Sunitha, V.}
\itemti{Automorphisms of augmented cubes.}
\itemso{Int. J. Comput. Math. 85, No. 11, 1621-1627 (2008).}
\itemab
In an earlier paper [Networks 40, 71--84 (2002; Zbl 1019.05052)], the authors defined a new family of graphs, called augmented cubes $AQ_n$, which generalize hypercubes but have several properties that the hypercubes (and other variations) do not. The definition of $AQ_n$ is easy: the vertex-set consists of all $n$-bit binary strings, and two such strings $A = a_{1}a_{2}\ldots a_{n}$ and $B = b_{1}b_{2}\ldots b_{n}$ are adjacent in $AQ_n$ if and only if either $A$ and $B$ differ in exactly one position, or agree in the first $k$ positions and differ in the remaining $n-k$ positions, for some $k \in \{0,1,\ldots,n-1\}$. In this paper the authors prove that for all $n \ge 4$, the automorphism group of $AQ_n$ has order $2^{n+3}$. They also show that $AQ_n$ is a Cayley graph for $(\mathbb{Z}_2)^n$, although that follows from their earlier observation that $(\mathbb{Z}_2)^n$ acts transitively (and hence regularly) on the vertices of $AQ_n$.
\itemrv{Marston Conder (Auckland)}
\itemcc{}
\itemut{hypercube; augmented cube; Cayley graph; automorphism}
\itemli{doi:10.1080/00207160701543384}
\end