A classification of primer hypermaps with a product of two primes number of hyperfaces. (May 2017)

• Record Type: Journal Article
• Authors: Du, Shaofei; Hu, Xinyuan
• Is Part Of: European journal of combinatorics. Volume 62(2017)
• Page Start: 245
• Page End: 262
• Publication Date: 2017-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2017.01.005
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: A hypermap is a cellular embedding of a connected bipartite graph G into a compact and connected surface S without border. The vertices of G lie in distinct partitions, colored black and white, and are called respectively the hypervertices and hyperedges of the hypermap, while the connected regions of G ∖ S are the hyperfaces. A hypermap H is called orientable if the underlying surface S is orientable. An orientable hypermap is called regular if its orientation preserving automorphism group G acts regularly on the flags (hypervertex, hyperedge and hyperface incident triples), and further, it is called (face-)primer if G induces a faithful action on their hyperfaces. In Breda d'Azevedo and Fernandes (2011), a classification of the primer hypermap with a prime number of hyperfaces is given. In this paper, a classification will be given, for all primer hypermaps with a product of two primes hyperfaces, seeTheorem 5.1 .