Recognizing Circulant Graphs of Prime Order in Polynomial Time Recognizing Circulant Graphs of Prime Order in Polynomial Time
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چکیده
1 Abstract In this paper we present a time-polynomial recognition algorithm for circulant graphs of prime order. A circulant graph G of order n is a Cayley graph over the cyclic group Z n : Equivalently, G is circulant ii its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent connguration A and, in particular, a Schur ring S isomorphic to A. A can be associated without knowing G to be circulant. If n is prime, then by investigating the structure of A either we are able to nd an appropriate ordering of the vertices proving that G is circulant or we are able to prove that a certain necessary condition for G being circulant is violated. The algorithm we propose in this paper is a recognition algorithm for cyclic association schemes. It runs in time polynomial in n.
منابع مشابه
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