文章基本信息
- 标题：On the First Eigenvalue of the Combinatorial Laplacian for a Graph
- 本地全文：下载
- 作者：Yoshiki OHNO ; Hajime URAKAWA
- 期刊名称：Interdisciplinary Information Sciences
- 印刷版ISSN：1340-9050
- 电子版ISSN：1347-6157
- 出版年度：1994
- 卷号：1
- 期号：1
- 页码：33-46
- DOI：10.4036/iis.1994.33
- 出版社：The Editorial Committee of the Interdisciplinary Information Sciences
- 摘要：The eigenvalues of the combinatorial Laplacian of graphs with boundaries and infinite graphs without boundary are studied. For a graph with boundary G =( V ∪∂ V , E ∪∂ E ), a sharp lower bound of the first eigenvalue λ1( G ) is given provided G satisfies a general condition, the so called non-separation property. For an infinite graph G without boundary, the bottom of the spectrum, i.e., the infimum of the spectrum of the combinatorial Laplacian of G , denoted λ0( G ), is estimated as
λ0( G ) ≤ ¼ μ( G )2exp(μ( G )),
where μ( G ) is the exponential growth of G . As a corollary, if G is subexponential, λ0( G )=0. On the contrary,λ0( G ) >0 is shown for a simply connected infinite graph G with degree ≥4 at each vertex. - 关键词：graph;combinatorial Laplacian;eigenvalue;exponential growth
