Abstract
In this paper we give a report on some results for the Star and Pancake graphs obtained after the conference Search Methodologies which was held in October, 2010. The graphs are defined as Cayley graphs on the symmetric group with the generating sets of all prefix---transpositions and prefix---reversals, correspondingly. They are also known as the Star and Pancake networks in computer science. In this paper we give the full characterization of perfect codes for these graphs. We also investigate a cycle structure of the Pancake graph and present an explicit description of small cycles as well as their number in the graph.
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