Extremal hexagonal chains concerning k-matchings and k-independent sets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Lian-zhu Zhang Fu-ji Zhang

Affiliation:	(1) Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian, 363000, China;(2) Department of Mathematics, Xiamen University, Xiamen, Fujian, 361005, China

Abstract:	Denote by _n the set of the hexagonal chains with n hexagons. For any B_n_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_n and for any k0, m_k(L_n)m_k(B_n)m_k(Z_n) and i_k(L_n)i_k(B_n)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.

Keywords:	hexagonal chain graph invariants benzenoid hydrocarbons k-matching k-independent set
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