The Adjacency Matrix and the Discrete Laplacian Acting on Forms

被引：0
作者：
Hatem Baloudi
Sylvain Golénia
Aref Jeribi
机构：
[1] Faculté Des Sciences De Sfax,
[2] Univ. Bordeaux,undefined
[3] Bordeaux INP,undefined
[4] CNRS,undefined
[5] IMB,undefined
[6] UMR 5251,undefined
来源：
Mathematical Physics, Analysis and Geometry | 2019年 / 22卷
关键词：
Discrete Laplacian; Locally finite graphs; Self-adjoint extension; Adjacency matrix; Forms; 81Q35; 47B25; 05C63;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We complete the understanding of the question of the essential self-adjoitness and non-essential self-adjointness of the discrete Laplacian acting on 1-forms. We also discuss the notion of completeness. Moreover, we study the relationship between the adjacency matrix of the line graph and the discrete Laplacian acting on 1-forms. Thanks to it, we exhibit a condition that ensures that the adjacency matrix on line graph is bounded from below and not essentially self-adjoint.
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