An efficient algorithm for generating all Kekulé patterns of a generalized benzenoid system

An algorithm for generating all Kekulé patterns of a benzenoid system was given by Jiang [1]. However, for a generalized benzenoid system, this problem is more complex. In this paper, we give an efficient algorithm for generating all Kekulé patterns of a generalized benzenoid system by the generalized directed tree structure [2] of the set of Kekulé patterns of a generalized benzenoid system.

[1]  M. Randic On the parity of Kekulé structures , 1977 .

[2]  M. Randic Aromaticity and conjugation , 1977 .

[3]  H. Wenjie,et al.  One-to-one correspondence between Kekulé and sextet patterns , 1986 .

[4]  I. Gutman,et al.  Graph theory and molecular orbitals , 1972 .

[5]  Rong-qin Sheng Identification of the Kekulé, structures of a hexagonal system , 1987 .

[6]  Ivan Gutman,et al.  Graph-theoretical analysis of the clar's aromatic sextet. Mathematical properties of the set of the kekulé patterns and the sextet polynomial for polycyclic aromatic hydrocarbons , 1981 .

[7]  E. Clar The aromatic sextet , 1972 .

[8]  Nenad Trinajstić,et al.  Kekule index for valence bond structures of conjugated polycyclic systems , 1973 .

[9]  Fuji Zhang,et al.  Mathematical properties and structures of sets of sextet patterns of generalized polyhexes , 1992 .

[10]  Zhi-bo Chen,et al.  Directed tree structure of the set of kekulé patterns of polyhex graphs , 1985 .

[11]  Haruo Hosoya,et al.  Sextet polynomial. A new enumeration and proof technique for the resonance theory applied to the aromatic hydrocarbons. , 1975 .

[12]  Milan Randic,et al.  A graph theoretical approach to conjugation and resonance energies of hydrocarbons , 1977 .

[13]  J. Aihara Aromatic sextets and aromaticity in benzenoid hydrocarbons. , 1977 .

[14]  Horst Sachs,et al.  Perfect matchings in hexagonal systems , 1984, Comb..

[15]  Milan Randic,et al.  A correlation between Kekulē valence structures and conjugated circuits , 1979 .

[16]  I. Gutman,et al.  On resonance theory , 1975 .

[17]  Guo Xiaofeng,et al.  Directed tree structure of the set of Kekule´ patterns of generalized polyhex graphs , 1991 .

[18]  M. L. Ellzey,et al.  Resonance theory. V. Resonance energies of benzenoid and nonbenzenoid .pi. systems , 1974 .

[19]  M. Randic Conjugated circuits and resonance energies of benzenoid hydrocarbons , 1976 .

[20]  Guo Xiaofeng,et al.  Recognizing Kekuléan benzenoid systems byC-P-V path elimination , 1990 .

[21]  M. Randic On the characterization of local aromatic properties in benzenoid hydrocarbons , 1974 .

[22]  Graph-theoretical analysis of the sextet polynomial. Proof of the correspondence between the sextet patterns and Kekulé patterns , 1990 .