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Isomorphism Problem for Metacirculant Graphs of Order a Product of Distinct Primes

Published online by Cambridge University Press:  20 November 2018

Edward Dobson
Edward Dobson*
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70808 USA
*
Current address: 401 Math Sciences, Oklahoma State University, Stillwater, OK 74078, USA email: [email protected]
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Abstract

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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 $\text{CI}$-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 $pq$.

Keywords

0520
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 6 , 01 December 1998 , pp. 1176 - 1188
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Alspach, B. and Parsons, T.D., Isomorphisms of circulant graphs and digraphs. DiscreteMath. 24(1979), 97–108.Google Scholar
2. Alspach, B., A construction for vertex-transitive graphs. Canad. J. Math. 24(1982), 307–318.Google Scholar
3. Babai, L., Isomorphism problem for a class of point-symmetric structures. Acta Math. Sci. Acad. Hung. 29(1977), 329–336.Google Scholar
4. Bollobàs, B., Graph Theory. Springer-Verlag, New York, 1979.Google Scholar
5. M, H.S.. Coxeter and Moser, W.O.T., Generators and Relations for Discrete Groups. Springer-Verlag, New York, 1965.Google Scholar
6. Hungerford, T., Algebra. Holt, Rinehart and Winston, 1974.Google Scholar
7. Ch, M.. Klin and Pöschel, R., The König problem, the isomorphism problem for cyclic graphs and the method of Schur. Proceedings of the Inter. Coll. on Algebraic methods in graph theory, Szeged, 1978. Coll. Mat. Soc. J´anos Bolyai 27.Google Scholar
8. Marušič, D., On vertex–transtive graphs of order qp. J. Combin. Math. Combin. Comput. 4(1988), 97–114.Google Scholar
9. Sabidussi, G.O., Vertex-transitive graphs. Monatsh. Math. 68(1964), 426–438.Google Scholar
10. Wielandt, H., Finite Permutation Groups. Academic Press, New York, 1964.Google Scholar