Spectral Analysis of Some Graphs with Infinite Rays - Lebid’, V. O.; Nizhnik, L. P. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
We perform a detailed spectral analysis of countable graphs formed by joining semibounded infinite chains to vertices of a finite graph. The spectrum of a self-adjoint operator generated by the adjacency matrix of the graph is characterized, the spectral measure is constructed, the eigenvectors are presented in the explicit form, and the spectral expansion in eigenvectors is obtained.