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The probability of connectedness of an unlabelled graph can be less for more edges. (English) Zbl 0254.05111


MSC:

05C30 Enumeration in graph theory
05C35 Extremal problems in graph theory
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References:

[1] N. G. de Bruijn, Applied combinatorial mathematics, (ed. E. F. Beckenback), Wiley, New York, 1964, Chap. 5.
[2] P. Erdős and A. Rényi, On random graphs. I, Publ. Math. Debrecen 6 (1959), 290 – 297. · Zbl 0092.15705
[3] L. Euler, Calcul de la probabilité dans le jeu de rencontre, Mem. Acad. Sci. Berlin 1753, 255-270; Opera Omnia (1) 7 (1923), 11-25.
[4] -, Solutio questionis curiosae ex doctrina combinationum, Mem. Acad. Sci. St. Petersbourg 3 (1811), 57-64; Opera Omnia (1) 7 (1923), 435-448.
[5] Frank Harary, The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc. 78 (1955), 445 – 463. · Zbl 0065.16702
[6] Frank Harary, Graph theory, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London, 1969. · Zbl 0182.57702
[7] Walter Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann. 174 (1967), 53 – 78 (German). · Zbl 0155.35002
[8] G. Pólya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math. 68 (1937), 147-254. · JFM 63.0547.04
[9] John Riordan, An introduction to combinatorial analysis, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. · Zbl 0078.00805
[10] E. M. Wright, Asymptotic enumeration of connected graphs, Proc. Roy. Soc. Edinburgh Sect. A 68 (1968/1970), 298 – 308. · Zbl 0188.55805
[11] E. M. Wright, Graphs on unlabelled nodes with a given number of edges, Acta Math. 126 (1970), 1 – 9. · Zbl 0204.57202
[12] -, Arithmetical properties of Euler’s rencontre number, J. London Math. Soc. 4 (1972), 437-442. · Zbl 0228.10010
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