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# Isomorphism problem for metacirculant graphs of order a product of distinct primes

Published:1998-12-01
Printed: Dec 1998
• Edward Dobson
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## Abstract

In this paper, we solve the isomorphism problem for metacirculant graphs of order $pq$ that are not circulant. To solve this problem, we first extend Babai's characterization of the CI-property to non-Cayley vertex-transitive hypergraphs. Additionally, we find a simple characterization of metacirculant Cayley graphs of order $pq$, and exactly determine the full isomorphism classes of circulant graphs of order $pq$.
 MSC Classifications: 05 - unknown classification 0520 - unknown classification 20