The Clar covering polynomial of hexagonal systems .1.

被引：122
作者：
Zhang, HP [1 ]
Zhang, FJ [1 ]
机构：
[1] XIAMEN UNIV,DEPT MATH,XIAMEN 361005,FUJIAN,PEOPLES R CHINA
来源：
DISCRETE APPLIED MATHEMATICS | 1996年 / 69卷 / 1-2期
关键词：
D O I：
10.1016/0166-218X(95)00081-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by its Clar covering polynomial. In addition, we give some theorems to calculate the Clar covering polynomial of a hexagonal system. As examples we finally derive the explicit expressions of the Clar covering polynomials for some small hexagonal systems and several types of catacondensed hexagonal systems. A relation between the resonance energy and the Clar covering polynomial of a hexagonal system is considered in the next paper.
引用
收藏
页码：147 / 167
页数：21
相关论文
共 17 条
  • [1] [Anonymous], 1989, MATCH-COMMUN MATH CO
  • [2] [Anonymous], J SERB CHEM SOC
  • [3] ALTERNATING 6-CYCLES IN PERFECT MATCHINGS OF GRAPHS REPRESENTING CONDENSED BENZENOID HYDROCARBONS
    BALABAN, AT
    TOMESCU, I
    [J]. DISCRETE APPLIED MATHEMATICS, 1988, 19 (1-3) : 5 - 16
  • [4] Clar E., 1972, AROMATIC SEXTET
  • [5] Cyvin S. J., 1988, LECT NOTES CHEM, V46
  • [6] FARREL EJ, 1979, J COMB THEORY B, V27, P111
  • [7] A REGULARITY IN HERNDON RESONANCE ENERGY METHOD
    GUTMAN, I
    ELBASIL, S
    [J]. CHEMICAL PHYSICS LETTERS, 1985, 115 (4-5) : 416 - 418
  • [8] GUTMAN I, 1989, INTRO THEORY BENZENO, P66
  • [9] GUTMAN I, 1983, GRAPH THEORY, P151
  • [10] GUTMAN I, 1982, B SOC CHIM BEOGRAD, V47, P453
12