Abstract
Moments (u k ) and coefficients of characteristic polynomials (a k ) have been evaluated in terms of molecular fragments up tok = 12 for bipartite Hückel graphs. Based on combinatorial analysis, each coefficient can be derived as a combination of binomial factors mapping to the corresponding multi-component graphs. The general formula becomes lengthy as k increases, but can be considerably simplified for a homologous series. This has been illustrated by dealing with the cata-condensed benzenoid hydrocarbons as a corollary where a rather compact set ofa k has been deduced. On combining the present result with Coulson's formula, one gains insight into the relative stability of isomers in relationship to the energy contribution of fragments classified as stabilized and destabilized species.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. Biggs,Algebraic Graph Theory (Cambridge University Press, Cambridge, 1974).
A. Graovac, I. Gutman and N. Trinajstić,Topological Approach to the Chemistry of Conjugated Molecules (Springer-Verlag, Berlin, 1977).
A.C. Tang, Y.S. Kiang, G.S. Yan and S.S. Dia,Graph Theoretical Molecular Orbitals (Science Press, Beijing, 1986); Y.S. Kiang, Int. J. Quant. Chem. S14(1980)541; 18(1980)331; S15(1981)293.
H. Hosoya, Bull. Chem. Soc. Japan 44 (1971)2332; Theor. Chem. Acta 25(1972)215; H. Hosoya and M. Randić, ibid. 63(1983)473; H. Hosoya and N. Ohkami, J. Comp. Chem. 4(1983)585.
H. Sachs, Publ. Math. Debrecen 11 (1963)119.
E. Heilbronner, Helv. Chim. Acta 36(1952)170.
I. Gutman, Chem. Soc. Faraday Trans. 2, 76 (1980)1161; I. Gutman, E.J. Rarrel and S.A. Wahid, J. Comb. Inf. Syst. Sci. 8(1983)159.
M.V. Kaulgud and V.H. Chitgopkar, J. Chem. Soc. Faraday Trans. 2, 73 (1977)1385; ibid. 74(1978)951.
M. Randić, J. Comp. Chem. 3 (1982)421.
K. Balasubramanian, Int. J. Quant. Chem. 21 (1982)581; K. Balasubramanian and M. Randić, Theor. Chim. Acta 61(1982)307.
B.J. McClelland, J. Chem. Soc. Faraday Trans. 2,78 (1982)991.
S. El-Basil, Theor. Chim. Acta 65 (1984)191; ibid. 64(1984)199.
J.R. Dias, Theor. Chim. Acta 68 (1985)107.
Y. Jiang and A. Tang, Int. J. Quant. Chem. 29 (1986)229.
Y. Jiang and H. Zhang, Theor. Chim. Acta 75 (1989)279.
Y. Jiang, A. Tang and R. Hoffmann, Theor. Chim. Acta 66 (1984)183.
W. Cao and Y. Jiang, Acta Chim. Sin. 40 (1982)880.
G.G. Hall, Theor. Chim. Acta 70 (1986)323.
A.T. Balaban,Chemical Applications of Graph Theory (Academic Press, London-New York-San Francisco, 1976) p. 73.
C.A. Coulson, Proc. Cambridge Phil. Soc. 36 (1940)201.
Author information
Authors and Affiliations
Additional information
received by the Publisher 20 September 1989
Rights and permissions
About this article
Cite this article
Jiang, Y., Zhang, H. Moments and characteristic polynomials of bipartite Hückel graphs. J Math Chem 3, 357–375 (1989). https://doi.org/10.1007/BF01169017
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01169017