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Enumeration of Locally Restricted Digraphs

Published online by Cambridge University Press:  20 November 2018

Frank Harary  and
Ed Palmer
Frank Harary
Affiliation:
The University of Michigan, Ann Arbor, Michigan
Ed Palmer
Affiliation:
The University of Michigan, Ann Arbor, Michigan
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Among the unsolved problems in graphical enumeration listed in (4) is included the determination of the number of graphs and digraphs with a given partition. Parthasarathy (9) has developed a formulation for counting graphs with a given partition by making a suitable modification of the method given in (2) for the enumeration of graphs. We present here an analogous modification that leads to a formula for the number of digraphs with a given partition. Not surprisingly, the main combinatorial device for this purpose is provided by the classical theorem due to Pólya.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 853 - 860
Copyright
Copyright © Canadian Mathematical Society 1966

References

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