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- Graph_enumeration abstract "In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the graph. The pioneers in this area of mathematics were Pólya, Cayley and Redfield.In some graphical enumeration problems, the vertices of the graph are considered to be labeled in such a way as to be distinguishable from each other, while in other problems any permutation of the vertices is considered to form the same graph. In general, labeled problems tend to be easier to solve than unlabeled problems. As with combinatorial enumeration more generally, the Pólya enumeration theorem is an important tool for dealing with symmetries such as this.Some important results in this area include the following.The number of labeled n-vertex undirected graphs is 2n(n − 1)/2.The number of labeled n-vertex directed graphs is 2n(n − 1).The number Cn of connected labeled n-vertex undirected graphs satisfies the recurrence relationfrom which one may easily calculate, for n = 1, 2, 3, ..., that the values for Cn are1, 1, 4, 38, 728, 26704, 1866256, ...(sequence A001187 in OEIS)The number of labeled n-vertex free trees is nn − 2 (Cayley's formula).The number of unlabeled n-vertex caterpillars is".
- Graph_enumeration thumbnail Cayley's_formula_2-4.svg?width=300.
- Graph_enumeration wikiPageID "9982439".
- Graph_enumeration wikiPageRevisionID "597641293".
- Graph_enumeration hasPhotoCollection Graph_enumeration.
- Graph_enumeration subject Category:Enumerative_combinatorics.
- Graph_enumeration subject Category:Graph_enumeration.
- Graph_enumeration comment "In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the graph.".
- Graph_enumeration label "Enumeración de grafos".
- Graph_enumeration label "Graph enumeration".
- Graph_enumeration sameAs Enumeración_de_grafos.
- Graph_enumeration sameAs m.02pyvtq.
- Graph_enumeration sameAs Q5597086.
- Graph_enumeration sameAs Q5597086.
- Graph_enumeration wasDerivedFrom Graph_enumeration?oldid=597641293.
- Graph_enumeration depiction Cayley's_formula_2-4.svg.
- Graph_enumeration isPrimaryTopicOf Graph_enumeration.