Eigenvalue cluster traces for quantum graphs with equal edge lengths (Q422038)

The paper investigates the eigenvalues and eigenfunctions of the Laplace operator \(\Delta\) on a finite metric graph with standard conditions and equal edge lengths. The author gives a necessary and sufficient condition for the existence of eigenvalues of \(\Delta\). Also results on the location of the eigenvalues of the Schrödinger operator \(\Delta+q\) near the existence of eigenvalues \(\lambda_n,\;n=1,2,\dots\), of \(\Delta\) are presented.