On the spectral radius of VDB graph matrices

Abstract

Introduction/purpose: Vertex-degree-based (VDB) graph matrices form a special class of matrices, corresponding to the currently much investigated vertex-degree-based (VDB) graph invariants. Some spectral properties of these matrices are investigated. Results: Generally valid sharp lower and upper bounds are established for the spectral radius of any VDB matrix. The equality cases are characterized. Several earlier published results are shown to be special cases of the presently reported bounds. Conclusion: The results of the paper contribute to the general spectral theory of VDB matrices, as well as to the general theory of VDB graph invariants.