Extremal hexagonal chains concerning k-matchings and k-independent sets

被引：47

作者：

Zhang, LZ ^{[1
]}

Zhang, FJ

机构：

[1] Zhangzhou Teachers Coll, Dept Math, Zhangzhou 363000, Fujian, Peoples R China

[2] Xiamen Univ, Dept Math, Xiamen 361005, Fujian, Peoples R China

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2000年 / 27卷 / 04期

基金：

中国国家自然科学基金;

关键词：

hexagonal chain; graph; invariants; benzenoid hydrocarbons; k-matching; k-independent set;

D O I：

10.1023/A:1018875823127

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

Denote by B-n, the set of the hexagonal chains with n hexagons. For any B-n is an element of B-n, let m(k)(B-n) and i(k)(B-n) be the numbers of k-matchings and k-independent sets of B-n, respectively. In the paper, we show that for any hexagonal chain B-n is an element of B-n and for any k greater than or equal to 0, m(k)(L-n) less than or equal to m(k)(B-n) less than or equal to m(k)(Z(n)) and i(k)(L-n) greater than or equal to i(k)(B-n) greater than or equal to i(k)(Z(n)), with left equalities holding for all k only if B-n = L-n, and the right equalities holding for all k only if B-n = Z(n), where L-n and Z(n) are the linear chain and the zig-zag chain, respectively. These generalize some related results known before.

引用

页码：319 / 329

页数：11