Circuit rank: Difference between revisions
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Revision as of 18:18, 28 May 2012
Template:Undirected graph numerical invariant
Definition
Definition for a finite graph
Suppose is a finite undirected graph. The circuit rank of , also called the cyclotomic number of , is defined in the following equivalent ways:
- It is the minimum number of edges that needs to be removed from the edge set of to make it a forest (i.e., an acyclic graph)
- It is given by where is the vertex set, is the edge set, and is the number of conncted components of .