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The Number of Ways to Label a Structure

Published online by Cambridge University Press:  01 January 2025

Frank Harary ,
Edgar M. Palmer  and
Ronald C. Read
Frank Harary
Affiliation:
University of Michigan University of the West Indies
Edgar M. Palmer
Affiliation:
University of Michigan University of the West Indies
Ronald C. Read
Affiliation:
University of Michigan University of the West Indies
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Abstract

It has been observed that the number of different ways in which a graph with p points can be labelled is p! divided by the number of symmetries, and that this holds regardless of the species of structure at hand. In this note, a simple group-theoretic proof is provided.

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 2 , June 1967 , pp. 155 - 156
Copyright
Copyright © 1967 The Psychometric Society

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Footnotes

*

This work was supported by Grant MH 10834 from the National Institute of Mental Health.

References

Harary, F. A seminar on graph theory, New York: Holt, Rinehart and Winston, 1967.Google Scholar
Harary, F. and Palmer, E. M. The power group of two permutation groups. Proceedings of the National Academy of Science, U. S. A., 1965, 54, 680–682.CrossRefGoogle ScholarPubMed
Harary, F. and Read, R. The probability of a given 1-choice structure. Psychometrika, 1966, 31, 271–278.Google ScholarPubMed
Katz, L. Probability of indecomposability of a random mapping function. Annals of Mathematical Statistics, 1955, 26, 512–517.Google Scholar