On the Problem of Determining which (n, k)-Star Graphs are Cayley Graphs
نویسندگان
چکیده
In this paper we work to classify which of the (n, k)-star graphs, denoted by Sn,k, are Cayley graphs. Although the complete classification is left open, we derive infinite and non-trivial classes of both Cayley and non-Cayley graphs. We give a complete classification of the case when k = 2, showing that Sn,2 is Cayley if and only if n is a prime power. Additionally, it is shown that Sn,n−2 is always Cayley and we give some sufficient conditions for Sn,3 to be Cayley. New structural results are developed, which may be useful in other contexts, and it is shown that Sn,k always has a uniform shortest path routing.
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عنوان ژورنال:
- Graphs and Combinatorics
دوره 33 شماره
صفحات -
تاریخ انتشار 2017