Isomorphism Problem for Metacirculant Graphs of Order a Product of Distinct Primes
Canadian journal of mathematics, Tome 50 (1998) no. 6, pp. 1176-1188

Voir la notice de l'article provenant de la source Cambridge University Press

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 $pq$ .
DOI : 10.4153/CJM-1998-057-5
Mots-clés : 05, 20
Dobson, Edward. Isomorphism Problem for Metacirculant Graphs of Order a Product of Distinct Primes. Canadian journal of mathematics, Tome 50 (1998) no. 6, pp. 1176-1188. doi: 10.4153/CJM-1998-057-5
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1998-057-5/}
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[1] 1. Alspach, B. and Parsons, T.D., Isomorphisms of circulant graphs and digraphs. DiscreteMath. 24(1979), 97–108. Google Scholar

[2] 2. Alspach, B., A construction for vertex-transitive graphs. Canad. J. Math. 24(1982), 307–318. Google Scholar

[3] 3. Babai, L., Isomorphism problem for a class of point-symmetric structures. Acta Math. Sci. Acad. Hung. 29(1977), 329–336. Google Scholar

[4] 4. Bollobàs, B., Graph Theory. Springer-Verlag, New York, 1979. Google Scholar

[5] 5. M, H.S.. Coxeter and Moser, W.O.T., Generators and Relations for Discrete Groups. Springer-Verlag, New York, 1965. Google Scholar

[6] 6. Hungerford, T., Algebra. Holt, Rinehart and Winston, 1974. Google Scholar

[7] 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 . Google Scholar

[8] 8. Marušič, D., On vertex–transtive graphs of order qp. J. Combin. Math. Combin. Comput. 4(1988), 97–114. Google Scholar

[9] 9. Sabidussi, G.O., Vertex-transitive graphs. Monatsh. Math. 68(1964), 426–438. Google Scholar

[10] 10. Wielandt, H., Finite Permutation Groups. Academic Press, New York, 1964. Google Scholar

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