A linear algorithm for obtaining the Laplacian eigenvalues of a cograph

Abstract

In this article, we give an O(n)O\left(n) time and space algorithm for obtaining the Laplacian eigenvalues of a cograph. This approach is more efficient as there is no need to directly compute the eigenvalues of Laplacian matrix related to this class of graphs. As an application, we use this algorithm as a tool for obtaining a closed formula for the number of spanning trees of a cograph.

Keywords

• cograph
• laplacian eigenvalues
• spanning trees
• 15a18
• 05c50
• 05c85