Spectral analysis of locally finite graphs with one infinite ray - Lebid, V. O.; Nizhnik, L. P. (Reports of the National Academy of Sciences of Ukraine, 2014)
A complete spectral analysis of countable graphs defined as the union of a finite graph and a semibounded infinite chain is given. The spectrum of the adjacency matrix of graphs is defined, a spectral measure is constructed, the eigenvectors and the spectral expansion in eigenvectors are presented.