Unboundedness of Adjacency Matrices of Locally Finite Graphs

被引：0
|
作者：
Sylvain Golénia
机构：
[1] Mathematisches Institut der Universität Erlangen-Nürnberg,
来源：
Letters in Mathematical Physics | 2010年 / 93卷
关键词：
47A10; 05C63; 05C50; 47B25; adjacency matrix; locally finite graphs; self-adjointness; unboundedness; semi-boundedness; spectrum; spectral graph theory;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note, we give an optimal condition to ensure it is also unbounded from below. We also consider the case of weighted graphs. We discuss the question of self-adjoint extensions and prove an optimal criterium.
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页码：127 / 140
页数：13
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