The hyper-star graph $HS(n,k)$ is defined as follows : its vertex-set is theset of $ {0,1} $-sequences of length $n$ with weight $k$, where the weight of asequence $v$ is the number of $1^,s$ in $v$, and two vertices are adjacent ifand only if one can be obtained from the other by exchanging the first symbolwith a different symbol (1 with 0, or 0 with 1) in another position. In this paper, we will find the automorphism groups of regular hyper-star andfolded hyper-star graphs. Then, we will show that, only the graphs HS(4,2) andFHS(4,2) are Cayley graphs.
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机译：超星形图$ HS（n，k）$的定义如下：其顶点集是长度为$ n $且权重为$ k $的$ {0,1} $序列的集合，其中，序列权重$ v $是$ v $中$ 1 ^，s $的数量，并且两个顶点相邻且当且仅当可以通过将第一个符号与另一个符号交换（1与0或0与1交换）来获得另一个顶点时，在另一个位置。在本文中，我们将找到正则超星形图和折叠超星形图的自同构群。然后，我们将显示，只有图HS（4,2）和FHS（4,2）是Cayley图。
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