Enumerating Typical Circulant Covering Projections Onto a Circulant Graph
Rongquan Feng, Jin Ho Kwak, Young Soo Kwon · SIAM Journal on Discrete Mathematics · 2005
Enumerating the isomorphism classes of several types of graph covering projections is one of the central research topics in enumerative topological graph theory (see [S. F. Du, D. Marusic, and A. O. Waller, J. Combin. Theory Ser. B, 74 (1998), pp. 276--290], [S. F. Du, J. H. Kwak, and M. Y. Xu, J. Combin. Theory Ser. B, 93 (2005), pp. 73--93], [R. Feng, J. H. Kwak, J. Kim, and J. Lee, SIAM J. Discrete Math., 11 (1998), pp. 265--272], [R. Feng. and J. H. Kwak, Discrete Math.}, 277 (2004), pp. 73--85], [C. D. Godsil and A. D. Hensel, J. Combin. Theory Ser. B., 56 (1992), pp. 205--238], [M. Hofmeister, Discrete Math., 143 (1995), pp. 87--97], [M. Hofmeister, SIAM J. Discrete Math., 8 (1995), pp. 51--61], [M. Hofmeister, SIAM J. Discrete Math., 11 (1998), pp. 286--292], [J. H. Kwak, J. Chun, and J. Lee, SIAM J. Discrete Math., 11 (1998), pp. 273--285], [J. H. Kwak and J. Lee, Canad. J. Math., 42 (1990), pp. 747--761], and [J. H. Kwak and J. Lee, Combinatorial and Computational Mathematics: Present and Future, (2001), pp. 97--161]). A covering projection is called circulant if its covering graph is circulant. A covering projection p from a Cayley graph ${\rm Cay} ({\cal A},X)$ onto another ${\rm Cay} ({\cal Q},Y)$ is called typical if the map $p: {\cal A}\rightarrow {\cal Q}$ on the vertex sets is a group homomorphism from ${\cal A}$ onto ${\cal Q}$. In [R. Feng. and J. H. Kwak, Discrete Math., 277 (2004), pp. 73--85], the authors enumerated the isomorphism classes of typical circulant double covering projections onto a circulant graph. As a continuation of this work, we enumerate in this paper the isomorphism classes of those covering projections of any folding number. An erratum to this article has been appended at the end of the pdf file.