On Cayley's enumeration of alkanes (or 4-valent trees)

Journal of Integer Sequences

Volumn 2, Issue 2, 1999, Pages

  Rains, E M ^a   Sloane, N J A ^a  

^a AT AND T LABS RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BICENTERED ALKANES; CAYLEY'S ENUMERATION; TYPOGRAPHICAL ERRORS;

DATABASE SYSTEMS; ERROR ANALYSIS; FORESTRY; FUNCTIONS; MOTIVATION; PUBLISHING;

PARAFFINS;

EID: 0142129851     PISSN: 15307638     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (25)

1. [BeLL98] F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. Univ. Press, 1998, see p. 290.
2. [BuS65] R. G. Busacker and T. L. Saaty, Finite Graphs and Networks, McGraw-Hill, NY, 1965, see p. 201.
3. [Cay75] A. Cayley, Ueber die analytischen Figuren, welche in der Mathematik Bäume genannt werden und ihre Anwendung auf die Theorie chemischer Verbindungen, Ber. deutsch. chem. Ges., 8 (1875), 1056-1059.
4. [Cay75a] A. Cayley, On the analytic forms called trees, with applications to the theory of chemical combinations, Reports British Assoc. Adv. Sci., 45 (1875), 257-305 = Math. Papers, Vol. 9, pp. 427-460 (seep. 451).
5. [Cay75a] A. Cayley, On the analytic forms called trees, with applications to the theory of chemical combinations, Reports British Assoc. Adv. Sci., 45 (1875), 257-305 = Math. Papers, Vol. 9, pp. 427-460 (seep. 451).
6. [Cay81] A. Cayley, On the analytical forms called trees, Amer. J. Math., 4 (1881), 266-268.
7. [Har69] F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
8. [HaN60] F. Harary and R. Z. Norman, Dissimilarity characteristic theorems for graphs, Proc. Amer. Math. Soc., 54 (1960), 332-334.
9. [HeB31] H. R. Henze and C. M. Blair, The number of isomeric hydrocarbons of the methane series, J. Amer. Chem. Soc., 53 (1931), 3077-3085.
10. 2n+2 zu bestimmen, Ber. deutsch. chem. Ges., 13 (1880), 792. [Both the author's name and the chemical formula are incorrect.]
11. 2n+2 zu bestimmen, Ber. deutsch. chem. Ges., 30 (1897), 2423-2426.
12. [Her98] F. Herrmann, Entgegnung, Ber. deutsch. chem. Ges., 31 (1898), 91.
13. [Led69] J. Lederberg, Topology of molecules, pp. 37-51 of The Mathematical Sciences, M.I.T. Press, Cambridge, MA, 1969.
14. [Los97] S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Ber. deutsch. chem. Ges., 30 (1897), 1917-1926.
15. [Los97a] S. M. Losanitsch, Bemerkungen zu der Hermannschen Mittheilung: Die Anzahl der isomeren Paraffine, Ber. deutsch. chem. Ges., 30 (1897), 3059-3060.
16. [Per32] D. Perry, The number of structural isomers of certain homologs of methane and methanol, J. Amer. Chem. Soc., 54 (1932), 2918-2920.
17. [Polya36] G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443.
18. [Polya37] G. Polya, Kombinatorische Abzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math. 68 (1937), 145-254. Translated as G. Polya and R. C. Read, Combinatorial Enumeration of Groups, Graphs and Chemical Compounds, Springer-Verlag, NY, 1987.
19. [Polya37] G. Polya, Kombinatorische Abzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math. 68 (1937), 145-254. Translated as G. Polya and R. C. Read, Combinatorial Enumeration of Groups, Graphs and Chemical Compounds, Springer-Verlag, NY, 1987.
20. [Rea76] R. C. Read, The enumeration of acyclic chemical compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Academic Press, NY, 1976.
21. [Rob75] R. W. Robinson, personal communication, 1975.
22. [RoHB76] R. W. Robinson, F. Harary and A. T. Balaban, The numbers of chiral and achiral alkanes and mono substituted alkanes, Tetrahedron, 32 (1976), 355-361.
23. [Sch75] H. Schiff, Zur Statistik chemischer Verbindungen, Ber. deutsch. chem. Ber., 8 (1875), 1542-1547.
24. [HIS] N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, NY, 1973.
25. [EIS] N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, published electronically at www.research.att.com/~njas/sequences/.