Classification of Topological Symmetry Groups of Kn

Erica Flapan; Blake Mellor; Ramin Naimi; Michael Yoshizawa

Classification of Topological Symmetry Groups of Kn

Erica Flapan, Blake Mellor, Ramin Naimi, Michael Yoshizawa

Loyola Marymount University

Research output: Other contribution

Abstract

In this paper we complete the classification of topological symmetry groups for complete graphs K_n by characterizing which K_n can have a cyclic group, a dihedral group, or a subgroup of D_m × D_m for odd m, as its topological symmetry group. Using this classification, one can algorithmically determine all possible topological symmetry groups of K_n for any n.

Original language	Undefined/Unknown
State	Published - Jan 1 2014

Publication series

Name	Mathematics, Statistics and Data Science Faculty Works

Access to Document

http://digitalcommons.lmu.edu/math_fac/180

Cite this

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title = "Classification of Topological Symmetry Groups of Kn",

abstract = "In this paper we complete the classification of topological symmetry groups for complete graphs Kn by characterizing which Kn can have a cyclic group, a dihedral group, or a subgroup of Dm × Dm for odd m, as its topological symmetry group. Using this classification, one can algorithmically determine all possible topological symmetry groups of Kn for any n.",

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AU - Mellor, Blake

AU - Naimi, Ramin

AU - Yoshizawa, Michael

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N2 - In this paper we complete the classification of topological symmetry groups for complete graphs Kn by characterizing which Kn can have a cyclic group, a dihedral group, or a subgroup of Dm × Dm for odd m, as its topological symmetry group. Using this classification, one can algorithmically determine all possible topological symmetry groups of Kn for any n.

AB - In this paper we complete the classification of topological symmetry groups for complete graphs Kn by characterizing which Kn can have a cyclic group, a dihedral group, or a subgroup of Dm × Dm for odd m, as its topological symmetry group. Using this classification, one can algorithmically determine all possible topological symmetry groups of Kn for any n.

M3 - Other contribution

T3 - Mathematics, Statistics and Data Science Faculty Works

ER -