Spectra of Graphs Resulting from Various Graph Operations and Products: a Survey

Abstract

Let G be a graph on n vertices and A(G), L(G), and |L|(G) be the adjacency matrix, Laplacian matrix and signless Laplacian matrix of G, respectively. The paper is essentially a survey of known results about the spectra of the adjacency, Laplacian and signless Laplacian matrix of graphs resulting from various graph operations with special emphasis on corona and graph products. In most cases, we have described the eigenvalues of the resulting graphs along with an explicit description of the structure of the corresponding eigenvectors.

Keywords

• graph operation
• eigenvalue
• spectrum
• laplacian spectrum
• signless laplacian spectrum
• corona
• 05c50
• 05c05
• 15a18