In this article the Sturm – Liouville boundary value problem on the graph Γ of a special structure is considered. The graph Γ has m edges, joined at one common vertex, and m vertices of degree 1. The boundary value problem is set by the Sturm – Liouville differential expression with real-valued potentials, the Dirichlet boundary conditions, and the standard matching conditions.This problem has a countable set of eigenvalues. We consider the so-called weight numbers, being the residues of the diagonal elements of the Weyl matrix in the eigenvalues.
