A Classification of Regular Embeddings of Graphs of Order a Product of Two Primes

Authors:
Shao-Fei Du;Jin Ho Kwak;Roman Nedela
Affiliations:
Department of Mathematics, Capital Normal University, Beijing 100037, People's Republic of China;Combinatorial and Computational Mathematics Center, Pohang University of Science and Technology, Pohang 790-784, Korea. jinkwak@postech.ac.kr;Institute of Mathematics and Informatics, Slovak Academy of Sciences, 974 00 Banská Bystrica, Slovakia
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2004

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Abstract

In this paper, we classify the regular embeddings of arc-transitive simple graphs of order pq for any two primes p and q (not necessarily distinct) into orientable surfaces. Our classification is obtained by direct analysis of the structure of arc-regular subgroups (with cyclic vertex-stabilizers) of the automorphism groups of such graphs. This work is independent of the classification of primitive permutation groups of degree p or degree pq for p ≠ q and it is also independent of the classification of the arc-transitive graphs of order pq for p ≠ q.