Spectra of infinite graphs with tails
Leonid Golinskii
TL;DR
This paper explicitly computes the spectra of infinite graphs formed by attaching infinite paths to finite graphs, providing a canonical form of their adjacency matrices and a complete solution for uniformly attached paths.
Contribution
It introduces a canonical form for the adjacency matrix of such infinite graphs and offers explicit spectral computations, advancing understanding of their spectral properties.
Findings
Explicit spectral formulas for infinite graphs with attached paths
Canonical form of the adjacency matrix for these graphs
Complete solution for graphs with uniform attached paths
Abstract
We compute explicitly (modulo solutions of certain algebraic equations) the spectra of infinite graphs obtained by attaching one or several infinite paths to some vertices of certain finite graphs. The main result concerns a canonical form of the adjacency matrix of such infinite graphs. A complete answer is given in the case when the number of attached paths to each vertex is the same.
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Taxonomy
TopicsMatrix Theory and Algorithms · Graph theory and applications · Spectral Theory in Mathematical Physics