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Kwak J.H., Lee J. — Enumeration of Graph Coverings and Surface Branched Coverings
Kwak J.H., Lee J. — Enumeration of Graph Coverings and Surface Branched Coverings

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Название: Enumeration of Graph Coverings and Surface Branched Coverings

Авторы: Kwak J.H., Lee J.

Аннотация:

Lots of graphs having a symmetry property can be described as cover-ings of simpler graphs. In this manuscript, we examine several enumeration problems for various types of nonisomorphic graph coverings of a graph and some of their applications to a group theory or to a surface theory. This manuscript is organized as follows. In chapter 1, we introduce basic concepts. In chapter 2, by using covering graph construction, we count the positive isomorphism classes of cycle permutation graphs, which is equal to the number of double cosets of the dihedral group Dn in the symmetric group Sn on n elements. In chapter 3, we count nonisomorphic (connected) coverings of a graph and, as its application, we have another recursive formula for the number of conjugacy classes of subgroups of given index of a finitely generated free group. In chapter 4, we count nonisomorphic regular coverings of a graph whose covering transformation groups are abelian and, as its application, we count subgroups of given index of free abelian groups. The same work is done in chapter 5 for regular coverings having dihedral voltage groups. In chapter 6, we discuss a general counting formula for regular coverings having any finite voltage group. In chapter 7, after discussing a combinatorial proof of Hurwitz theorem for surface branched coverings, we consider the number of subgroups of surface groups. Finally, in chapter 8, we discuss a distribution of branched surface coverings of surfaces and some related topological properties including a generalization of the classical Alexander theorem.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 81

Добавлена в каталог: 12.12.2010

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Предметный указатель
Automorphism      1
Betti number      1
Bouquet of m circles      53
Burnside      3
Concrete      44
Concrete regular      44
Conjugacy      15
Connected      11
Covering      1
Covering isomorphism      2
Covering transformation group      2
Cycle permutation graphs      5
Derived embedding scheme      51
Embedding      50
Embedding scheme      50
Faces      50
Graph      1
Hurwitz system      57
Identity component      29
Isomorphic      1
Isomorphism      1
Liskovets      16
Local voltage group      29
Mobius function      23
Monodromy representation      57
Mutually orthogonal      3
n-fold covering      1
Neighborhood      1
Normalized      9
Ordinary voltage assignment      2
Permutation derived graph      2
Permutation voltage assignment      2
Positive natural isomorphism      6
Region      50
Regular      1
Rotation scheme      50
Schreier system      16
Similar      10
Standard presentation      54
Transitive      15
Vertex      1
Voltage assignment      50
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