Geodesic
The Number of -Coloured Graphs
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1344-1352

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we describe an algorithm for finding the number of non-isomorphic -coloured graphs with n nodes and e edges. We use Pόlya's fundamental enumeration theorem (in a form similar to that given by de Bruijn (see 1)) which reduces the problem to finding the cycle index for a certain permutation group. Harary (3) followed this same program for bi-coloured graphs, but failed to find the cycle index of the relevant group for general -coloured graphs. 
Klarner, David A. The Number of -Coloured Graphs. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1344-1352. doi: 10.4153/CJM-1968-134-x
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[1] 1. Beckenbach, Edwin F. (editor), Applied combinatorial mathematics, Chapter 5, “Pôlya's theory of counting”, by de Bruijn, N. G. pp. 144–184 (Wiley, New York, 1964). Google Scholar

[2] 2. de Bruijn, N. G. Generalization of Pôlya's fundamental theorem in enumerative combinatorial analysis, Nederl. Akad. Wetensch. Proc. Ser. A 62 Indag. Math. 21 (1959), 59–69. Google Scholar

[3] 3. Harary, F., On the number of bi-colored graphs, Pacific J. Math. 8 (1958), 743–755. Google Scholar

[4] 4. Read, R. C., The number of k-coloured graphs on labelled nodes, Can. J. Math. 12 (1960), 410–414. Google Scholar

[5] 5. Robinson, R. W., Enumeration of colored graphs, J. Combinatorial Theory 4 (1968), 181–190. Google Scholar

[6] 6. Wright, E. M., Counting coloured graphs. I, Can. J. Math. 13 (1961), 683–693. Google Scholar

[7] 7. Wright, E. M., Counting coloured graphs. II, Can. J. Math. 16 (1964), 128–135. Google Scholar

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