关于科林-德-韦尔迪埃图数和便士图

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-10-31 DOI:10.1016/j.laa.2024.10.026

A.Y. Alfakih

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引用次数: 0

摘要

图 G 的 Colin de Verdière 数（用 μ(G)表示）是图 G 的谱不变量，与图 G 的某些拓扑特性有关。例如，如果 G 是平面图，μ(G)≤3。一分钱图是平面上内部相交的等辐圆盘的接触图。在本论文中，我们将证明当补集 G‾ 是便士图时，μ(G) 的下界。

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On the Colin de Verdière graph number and penny graphs

The Colin de Verdière number of graph G, denoted by

μ (G)

, is a spectral invariant of G that is related to some of its topological properties. For example,

μ (G) \leq 3

iff G is planar. A penny graph is the contact graph of equal-radii disks with disjoint interiors in the plane. In this note, we prove lower bounds on

μ (G)

when the complement

\overline{G}

is a penny graph.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.