NDLI: Regular maps of graphs of order 4p

Content Provider	Springer Nature Link
Author	Zhou, Jin Xin Feng, Yan Quan
Copyright Year	2011
Abstract	A 2-cell embedding f: X → S of a graph X into a closed orientable surface S can be described combinatorially by a pair $$\mathcal{M} = (X;\rho )$$ called a map, where ρ is a product of disjoint cycle permutations each of which is the permutation of the arc set of X initiated at the same vertex following the orientation of S. It is well known that the automorphism group of $$\mathcal{M}$$ acts semi-regularly on the arc set of X and if the action is regular then the map $$\mathcal{M}$$ and the embedding f are called regular. Let p and q be primes. Du et al. [J. Algebraic Combin., 19, 123–141 (2004)]_classified the regular maps of graphs of order pq. In this paper all pairwise non-isomorphic regular maps of graphs of order 4p are constructed explicitly and the genera of such regular maps are computed. As a result, there are twelve sporadic and six infinite families of regular maps of graphs of order 4p; two of the infinite families are regular maps with the complete bipartite graphs K 2p,2p as underlying graphs and the other four infinite families are regular balanced Cayley maps on the groups ℤ4p , ℤ 2 2 × ℤ p and D 4p .
Ending Page	1012
Page Count	24
Starting Page	989
File Format	PDF
ISSN	14398516
e-ISSN	14397617
Journal	Acta Mathematica Sinica, English Series
Issue Number	5
Volume Number	28
Language	English
Publisher	Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Publisher Date	2011-09-30
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Planar graphs; geometric and topological aspects of graph theory Regular map Graphs and abstract algebra (groups, rings, fields, etc.) Finite automorphism groups of algebraic, geometric, or combinatorial structures algebraic map Cayley map 2-cell embedding Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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