Some comments on the eigenspaces of graphs

Dragos M. Cvetkovi{\cj}

Abstract: We continue the investigations on the relations between eigenvalues, eigenspaces and the structure of graphs. The angles between eigenspaces and the axes of a standard basis of $\R^n$ play an important role. A general problem is how to construct graphs with the given eigenvalues and angles. In particular, we treat connectivity and metric properties, reconstruction of unicyclic and bicyclic graphs, etc. The results are mostly of an algorithmic character rather than in form of explicit characterization theorems. Therefore we propose to treat these problems with the aid of a computer using artificial intelligence means.

Classification (MSC2000): 05C50

Full text of the article: