Petersen graph: Difference between revisions
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# It is the [[defining ingredient::complement of a graph|complement]] of the [[defining ingredient::line graph]] of [[defining ingredient::complete graph:K5]]. | # It is the [[defining ingredient::complement of a graph|complement]] of the [[defining ingredient::line graph]] of [[defining ingredient::complete graph:K5]]. | ||
# It is the [[defining ingredient::Kneser graph]] <math>KG_{5,2}</math>: its vertices are identified with subsets of size two of a 5-element set, and two vertices are adjacent if and only if the corresponding subsets are disjoint. | # It is the [[defining ingredient::Kneser graph]] <math>KG_{5,2}</math>: its vertices are identified with subsets of size two of a 5-element set, and two vertices are adjacent if and only if the corresponding subsets are disjoint. | ||
# It is the unique 5-[[defining ingredient::cage]]. | |||
Revision as of 18:11, 28 May 2012
This article defines a particular undirected graph, i.e., the definition here determines the graph uniquely up to graph isomorphism.
View a complete list of particular undirected graphs
Definition
The Petersen graph is a particular undirected graph on 10 vertices that can be defined in the following equivalent ways:
- It is the complement of the line graph of complete graph:K5.
- It is the Kneser graph : its vertices are identified with subsets of size two of a 5-element set, and two vertices are adjacent if and only if the corresponding subsets are disjoint.
- It is the unique 5-cage.
