论文信息 - Topological analysis of eigenvectors of the adjacency matrices in graph theory: The concept of internal connectivity

Topological analysis of eigenvectors of the adjacency matrices in graph theory: The concept of internal connectivity

Abstract The topological properties of eigenvectors of adjacency matrices of a graph have been analyzed. Model systems studied are n -vertex- m -edge ( n -V- m -E) graphs where n = 2–4, m = 1–6. The topological information contained in these eigenvectors is described using vertex-signed and edge-signed graphs. Relative ordering of net signs of edge-signed graphs is similar to that of eigenvalues of the adjacency matrix. This simple analysis has also been applied to naphthalene, anthracene and pyrene. It provides a sound basis for the application of graph theory to molecular orbital theory.

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