Graph enumeration

The complete list of all free trees on 2, 3, and 4 labeled vertices: tree with 2 vertices, trees with 3 vertices, and trees with 4 vertices.

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.[1] These problems may be solved either exactly (as an algebraic enumeration problem) or asymptotically. The pioneers in this area of mathematics were George Pólya,[2] Arthur Cayley[3] and J. Howard Redfield.[4]

  1. ^ Harary, Frank; Palmer, Edgar M. (1973). Graphical Enumeration. Academic Press. ISBN 0-12-324245-2.
  2. ^ Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen. Acta Math. 68 (1937), 145-254
  3. ^ "Cayley, Arthur (CLY838A)". A Cambridge Alumni Database. University of Cambridge.
  4. ^ The theory of group-reduced distributions. American J. Math. 49 (1927), 433-455.