Spectra of infinite graphs with tails
classification
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math.SP
keywords
graphsinfinitecertainpathsspectraadjacencyalgebraicanswer
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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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