Spectra of infinite graphs with tails |
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| Authors: | L Golinskii |
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| Institution: | 1. Mathematics Division, Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine.golinskii@ilt.kharkov.ua |
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| 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 given finite graphs. The main result concerns a canonical form for the adjacency matrix of such infinite graphs, and the algorithm of its calculation. The argument relies upon the spectral theory of eventually free Jacobi matrices. We also study some other couplings of infinite graphs (stars and Bethe–Caley trees). |
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| Keywords: | infinite graphs adjacency operator spectrum Jacobi matrices of finite rank Jost function |
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