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Enumeration of acyclic and unicyclic nets with four types of self‐duality
Author(s) -
Holroyd Fred
Publication year - 1983
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190070214
Subject(s) - combinatorics , enumeration , mathematics , dual polyhedron , net (polyhedron) , graph , duality (order theory) , discrete mathematics , geometry
A net is a graph in which each point and line is given a sign. The point, line, and simple duals of a net are obtained by reversing the signs of the points, lines, or both. If a net possesses two of the three types of self‐duality, it possesses all three and is said to be doubly self‐dual. Enumeration formulas are derived for nets and point, line, simply, and doubly self‐dual nets, whose underlying graphs are acyclic and unicyclic. The numbers are tabulated up to 12 points (24 for doubly self‐dual nets) in each case.