Vipul: /* Alternate definitions */

2012-05-29T04:29:49Z

Alternate definitions

← Older revision		Revision as of 04:29, 29 May 2012
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	The '''Tutte-Coxeter graph''' can also be defined in the following equivalent ways:		The '''Tutte-Coxeter graph''' can also be defined in the following equivalent ways:

	# It is the [[defining ingredient::Levi graph]] corresponding to the [[defining ingredient::Cremona-Richmond configuration]].		# It is the [[defining ingredient::Levi graph]] corresponding to the [[defining ingredient::Cremona-Richmond configuration]], which in turn is the generalized quadrangle with parameters (2,2).
	# It is the unique (up to [[graph isomorphism]]) (3,8)-[[defining ingredient::cage]].		# It is the unique (up to [[graph isomorphism]]) (3,8)-[[defining ingredient::cage]].

Vipul: Created page with "{{particular undirected graph}} ==Definition== ===Definition in terms of duads and synthemes=== Consider a fixed set of size 6. Define the ''duads'' as the subsets of size ..."

2012-05-29T04:28:59Z

Created page with "{{particular undirected graph}} ==Definition== ===Definition in terms of duads and synthemes=== Consider a fixed set of size 6. Define the ''duads'' as the subsets of size ..."

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{{particular undirected graph}}

==Definition==

===Definition in terms of duads and synthemes===

Consider a fixed set of size 6. Define the ''duads'' as the subsets of size 2 of this set. There are <math>\binom{6}{2} = 15</math> duads. Define the ''synthemes'' as the partitions of the set into triples of subsets of size 2. There are <math>\frac{1}{3!}\binom{6}{2,2,2} = 15</math> synthemes.

The Tutte-Coxeter graph is defined as follows:

# Its vertex set is the union of the set of duads and the set of synthemes
# Its edges are defined as follows: two vertices are adjacent if one of them is a duad, the other is a syntheme, and the duad is one of the three pieces in the partition described by the syntheme.

===Alternate definitions===

The '''Tutte-Coxeter graph''' can also be defined in the following equivalent ways:

# It is the [[defining ingredient::Levi graph]] corresponding to the [[defining ingredient::Cremona-Richmond configuration]].
# It is the unique (up to [[graph isomorphism]]) (3,8)-[[defining ingredient::cage]].

Tutte-Coxeter graph - Revision history

Vipul: /* Alternate definitions */

Vipul: Created page with "{{particular undirected graph}} ==Definition== ===Definition in terms of duads and synthemes=== Consider a fixed set of size 6. Define the ''duads'' as the subsets of size ..."