Abstract
This paper presents a few novel results, and collects together what is known and conjectured about the branching graph of a polyhex.
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References
E.C. Kirby, J. Math. Chem. 4 (1990) 31; 8 (1991) 77.
E.C. Kirby, J. Math. Chem. l (1987)175.
R.B. Mallion, Proc. Roy. Soc. A 341 (1975)429; Chem. Phys. Lett. 36 (1975) 170.
J. Gayoso and A. Boucekkine, Compt. Rend. Acad. Sci. (Paris) C 272 (1971)184.
R. McWeeny, Mol. Phys. l (1958)311.
R.B. Mallion, Mol. Phys. 25 (1973)1415.
C.W. Haigh and R.B. Mallion, Prog. NMR Spectry. 13 (1979)303.
J. Aihara, J. Am. Chem. Soc. 101 (1979)5913; Bull. Chem. Soc. Japan 54 (1981) 1245; 58 (1985)1045;59(1986)3781; J. Aihara and T. Horikawa, Bull. Chem. Soc. Japan 56 (1983) 1853.
A. Baba Ahmed and J. Gayoso, Int. J. Quant. Chem. 23 (1983)71.
B. O'Leary and R.B. Mallion, J. Math. Chem. 3 (1989)323.
N. Mizoguchi, Bull. Chem. Soc. Japan 60 (1987)2005.
C.W. Haigh and R.B. Mallion, Croat. Chem. Acta 62 (1989)1.
E.C. Kirby, J. Chem. Soc. Faraday Trans. 86 (1990)447.
J.R. Dias, Thermochim. Acta 122 (1987)313; J. Chem. Inf. Comput. Sci. 31 (1991) 89.
J.V. Knop, W.R. Müller, K. Szymanski and N. Trinajstić, J. Comput. Chem. 7 (1986)547.
R.J. Wilson,Introduction to Graph Theory, 3rd Ed. (Longman, New York, 1988).
A.T. Balaban and F. Harary, Tetrahedron 24 (1968)2505.
A.T. Balaban, Pure Appl. Chem. 54 (1985)335.
I. Gutman and S.J. Cyvin,Introduction to the Theory of Benzenoid Hydrocarbons (Springer, Berlin, 1989).
N. Trinajstić, J. Math. Chem. 5 (1990)171.
N. Trinajstić,Chemical Graph Theory, 2nd Ed. (CRC Press, Boca Raton, 1992).
I. Gutman and E.C. Kirby, MATCH 26 (1991)111.
C. Berge,Graphs and Hypergraphs (North-Holland, Amsterdam, 1973).
L. Lovász and M.D. Plummer,Matching Theory (North-Holland, Amsterdam, 1986).
S.J. Cyvin and I. Gutman,Kekulé Structures in Benzenoid Hydrocarbons (Springer, Berlin, 1988).
I. Gutman, Topics Current Chem. 162 (1992)1.
E.C. Kirby, R.B. Mallion and P. Pollak, J. Chem. Soc. Faraday Trans., in press; E.C. Kirby, Croat. Chem. Acta, in press.
I. Gutman, Croat. Chem. Acta 46 (1974)209.
C.E. Soteros and S.G. Whittington, J. Math. Chem. 5 (1990)307.
E.C. Kirby, J. Math. Chem. ll (1992)187.
J.R. Dias, J. Chem. Inf. Comput. Sci. 22 (1982)15.
J.R. Dias, J. Mol. Struct. (THEOCHEM) 137 (1986)9.
I. Gutman and J.R. Dias, in: R. Bodendiek (ed.),Contemporary Methods in Graph Theory (BI-Wissenschaftsverlag, Mannheim, 1990) pp.249–259.
J.R. Dias, MATCH 26 (1991)87.
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Kirby, E.C., Gutman, I. The branching graphs of polyhexes: Some elementary theorems, conjectures and open questions. J Math Chem 13, 359–374 (1993). https://doi.org/10.1007/BF01165575
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DOI: https://doi.org/10.1007/BF01165575