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2010 Roundness properties of graphs
Matthew Horak, Eric LaRose, Jessica Moore, Michael Rooney, Hannah Rosenthal
Involve 3(1): 67-91 (2010). DOI: 10.2140/involve.2010.3.67


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 7, 8 and 9 vertices. We also show that no connected graph can have roundness between log23 and 2.


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Matthew Horak. Eric LaRose. Jessica Moore. Michael Rooney. Hannah Rosenthal. "Roundness properties of graphs." Involve 3 (1) 67 - 91, 2010.


Received: 27 July 2009; Revised: 28 December 2009; Accepted: 29 December 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1230.05157
MathSciNet: MR2672502
Digital Object Identifier: 10.2140/involve.2010.3.67

Primary: 05C99
Secondary: 20F65, 46B20

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.3 • No. 1 • 2010
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