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Roundness
properties of graphs
Matthew Horak, Eric LaRose, Jessica Moore, Michael Rooney and Hannah Rosenthal
Vol. 3 (2010), No. 1, 67–91
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Abstract |
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The notion of the roundness of a metric space was introduced by Per Enflo as a tool to study geometric properties of Banach spaces. Recently, roundness and generalized roundness have been used in the context of group theory to investigate relationships between the geometry of a Cayley graph of a group and the algebraic properties of the group. In this paper, we study roundness properties of connected graphs in general. We explicitly calculate the roundness of members of two classes of graphs and we give results of computer calculations of the roundness of all connected graphs on , and vertices. We also show that no connected graph can have roundness between and . |
Keywords
roundness, graph, metric invariant
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Mathematical Subject Classification 2000
Primary: 05C99
Secondary: 46B20, 20F65
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Milestones
Received: 27 July 2009
Revised: 28 December 2009
Accepted: 29 December 2009
Published: 20 April 2010
Communicated by Scott Chapman
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Authors |
| Matthew Horak | |
| Mathematics, Statistics and Computer
Science Department University of Wisconsin – Stout Menomonie, WI 54751 United States |
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| http://faculty.uwstout.edu/horakm/ | |
| Eric LaRose | |
| Mathematics, Statistics and Computer
Science Department University of Wisconsin – Stout Menomonie, WI 54751 United States |
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| Jessica Moore | |
| Mathematics, Statistics and Computer
Science Department University of Wisconsin – Stout Menomonie, WI 54751 United States |
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| Michael Rooney | |
| Mathematics, Statistics and Computer
Science Department University of Wisconsin – Stout Menomonie, WI 54751 United States |
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| Hannah Rosenthal | |
| Mathematics, Statistics and Computer
Science Department University of Wisconsin – Stout Menomonie, WI 54751 United States |
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