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The Number of Coloured Graphs

Published online by Cambridge University Press:  20 November 2018

L. Carlitz
L. Carlitz*
Affiliation:
Duke University
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Let Fn(k) denote the total number of k-coloured graphs on n labelled nodes and let Mn(k) denote the number of graphs on n nodes that are coloured in at most kcolours ; also let fn(k) denote the number of connected k coloured graphs on n nodes. Read (3) has proved the following formulas:

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 304 - 312
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Carlitz, L., A note on Rummer's congruence, Arch, der Math., 7 (1956), 441–445.Google Scholar
2. Carlitz, L. and Riordan, J., The number of labeled two-terminal series-parallel networks, Duke Math. J., 23 (1956), 435–445.Google Scholar
3. Read, R. C., The number of k-coloured graphs on labelled nodes, Can. J. Math., 12 (1960), 410–414.Google Scholar
4. Wright, E. M., Counting coloured graphs, Can. J. Math., 15 (1961), 683–693.Google Scholar