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Enumeration of self-converse digraphs

Published online by Cambridge University Press:  26 February 2010

F. Harary and
E. M. Palmer
F. Harary
Affiliation:
The University of Michigan.
E. M. Palmer
Affiliation:
The University of Michigan.
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Extract

How many digraphs are isomorphic with their own converses? Our object is to derive a formula for the counting polynomial dp′(x) which has as the coefficient of xq, the number of “self-converse” digraphs with p points and q lines. Such a digraph D has the property that its converse digraph D′ (obtained from D by reversing the orientation of all lines) is isomorphic to D. The derivation uses the classical enumeration theorem of Pólya [9[ as applied to a restriction of the power group [6] wherein the permutations act only on 1–1 functions.

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Type
Research Article
Information
Mathematika , Volume 13 , Issue 2 , December 1966, pp. 151 - 157
Copyright
Copyright © University College London 1966

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References

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