A note on the multiplicities of the eigenvalues of a graph

Abstract

Let A(G) be a Hermitian matrix whose graph is a given graph G. From the interlacing theorem, it is known that mA(G\1)(θ) ≥ mA(G)(θ) is the multiplicity of the eigenvalue???of A(G). In this note we improve this inequality for some paths with more than one vertex.