路或圈的笛卡尔乘积图的支撑树数

数学物理学报 ›› 2003, Vol. 23 ›› Issue (1): 70-76.

路或圈的笛卡尔乘积图的支撑树数

陈协彬

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漳州师范学院数学系

出版日期:2003-02-25 发布日期:2003-02-25
基金资助:
福建省自然科学基金项目

The Numbers of Spanning Trees in the Cartesian ProductGraphs of Paths or Cycles

CHEN Xie-Ban

Online:2003-02-25 Published:2003-02-25
Supported by:
福建省自然科学基金项目

摘要/Abstract

摘要：

设G是路或圈的笛卡尔乘积图，t(G)表示G的支撑树数.该文借助于第二类Chebyshev多项式给出t(G)的公式，并考虑了t(G)的线性递归关系及渐近性态.

关键词: 支撑树；Laplace谱；第二类Chebyshev多项式；线性递归关系

Abstract:

Let G be the Cartesian product graph of paths or cycles, and let t(G)denote the number of spanning trees in G. In this paper, the formula for t(G) is given by means of Chebyshev polynomial of the second kind, and the linear recurrence relation and the asymptotic behavior of t(G) are considered.

Key words: Spanning tree, Laplacian spectrum, Chebyshev polynomial of the second kindLinear , recurrence , relation

中图分类号:

05C05

陈协彬. 路或圈的笛卡尔乘积图的支撑树数[J]. 数学物理学报, 2003, 23(1): 70-76.

CHEN Xie-Ban. The Numbers of Spanning Trees in the Cartesian ProductGraphs of Paths or Cycles[J]. Acta mathematica scientia,Series A, 2003, 23(1): 70-76.