Enumeration of Locally Restricted Digraphs
- 1 January 1966
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 18, 853-860
- https://doi.org/10.4153/cjm-1966-085-5
Abstract
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.Keywords
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