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Enumeration Of Labelled Graphs

Published online by Cambridge University Press:  20 November 2018

E. N. Gilbert*
Affiliation:
Bell Telephone Laboratories, Murray Hill, NJ.
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1. Introduction. The number of connected linear graphs having V vertices labelled 1, … , V and λ (unlabelled) lines is found below. Similar formulas are found for graphs in which slings, lines “in parallel,” or both are allowed and for directed graphs with or without slings or parallel lines. Some of these graphs are also counted when the lines are labelled and the vertices are unlabelled.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Bell, E. T., Exponential polynomials, Ann. Math., 35 (1934), 258277.Google Scholar
2. Bell, E. T., Postulational bases for the umbral calculus, Amer. J. Math., 62 (1940), 717724.Google Scholar
3. Davis, R. L., The number of structures of finite relations, Proc. Amer. Math. Soc, 4 (1953), 486495.Google Scholar
4. Harary, F., The number of linear, directed, rooted and connected graphs, Trans. Amer. Math. Soc, 78 (1955), 445463.Google Scholar
5. Jordan, C., Calculus of Finite Differences (New York, 1950).Google Scholar
6. Kaplansky, I. and Riordan, J., Multiple matching and runs by the symbolic method, Ann. Math. Stat. (3), 16 (1945), 272277.Google Scholar
7. König, D., Theorie der endlichen und unendlichen Graphen (New York, 1950).Google Scholar
8. Netto, E., Lehrbuch der Combinatorik (Leipzig, 1901).Google Scholar
9. Riddell, R. J., Jr. and Uhlenbeck, G. E., On the theory of the virial development of the equation of state of monoatomic gases, J. Chem. Phys., 21 (1953), 20562064.Google Scholar