Abstract
Clar structures recently used as basis-set to compute resonance energies [9] are identified as maximal independent sets of benzenoid hydrocarbons “colored” in a special way. Binomial properties of such objects are induced for several catafusenes and perifusenes (Eqs. 2–31). Novel polynomials, called Clar polynomials, are given for perifusens in terms of units of catafusenes which allow display and enumeration of the populations of their Clar structures. The work is particularly pertinent to that of [8] and [9].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Herndon WC (1973) J Am Chem Soc 95:2404; (1980) 102:1538; Herndon WC, Ellzey Jr ML; (1974), J Am Chem Soc 96:6631 and numerous subsequent publications
Randić M (1976) Chem Phys Letters 38:68; (1977) J Am Chem Soc 99:444; (1977) Tetrahedron 33:1906; (1977) Mol Phys 34:849
Gomes JAFN (1979) Rev Port Quim 21:82; (1980) Croat Chem Acta 53:561; (1980) Theor Chim Acta 59:333
Hosoya H, Yamaguchi T (1975) Tetrahedron Letters 4659
Clar E (1972) The aromatic sextet. Wiley, New York
See, e.g., Gutman (1982) Bull Soc Chim Beograd 47:464
Ohkami N, Motoyama A, Yamaguchi T, Hosoya H, Gutman I (1981) Tetrahedron 37:1113
Ohkami N, Hosoya H (1983) Theor Chim Acta 64:153
Herndon WC, Hosoya H (1984) Tetrahedron 40:3987
Dewar MJS, De Llano C (1969) J Am Chem Soc 91:789
A good source may be found in: Trinajstić N (1983) Chemical graph theory, vol II, chapt 10. The Chemical Rubber Company Press, Boca Raton
A method has been developed recently for the calculation of the number of those Kekule structures of a benzenoid hydrocarbon which are represented by its Clar formulas: Gutman I, Obenland S, Schmidt W (1985) Match 17:75
Gutman I (1982) Z Naturforsch 37a:69; Gutman I, El-Basil S (1984) Z Naturforsch 39a:276
Christofisdes N (1975) Graph theory. An algorithmic approach, chapt 3. Academic Press, New York
See, e.g., El-Basil S (1983) Bull Chem Soc Japan 56:3152
El-Basil S: Binomial properties of Clar structures. Submitted for publication in Discrete Applied Mathematics
Cohen DA (1978) Basic techniques of combinatorial theory. Wiley, New York
Balaban AT, Tomescu I (1984) Croat Chem Acta 57:391
Hosoya H (1973) Fibonacci Quart 11:255; El-Basil S (1984) Theor Chim Acta 65:191; Gutman I, El-Basil S (1985) Chem Phys Letters 115:416, Gutman I, El-Basil S; Fibonacci graphs. Unpublished results
Gutman I (1985) Match 17:3
The term skeletal graph is used in: Aida M, Hosoya H (1980) Tetrahedron 36:1321
See, e.g., Harary F (1972) Graph theory Addison-Wesely, Reading Mass
Randić seems to be the first who expressed a counting polynomial of a graph in terms of those of much simpler graphs: Randić M, (1983) Theor Chim Acta 62:485
Author information
Authors and Affiliations
Additional information
This paper is dedicated to Professor Eric Clar; the Doyen of aromatic chemistry.
Rights and permissions
About this article
Cite this article
El-Basil, S. Combinatorial Clar sextet theory. Theoret. Chim. Acta 70, 53–65 (1986). https://doi.org/10.1007/BF00531152
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00531152