BOUNDS ON THE FIRST NONZERO EIGEN-VALUE FOR SELF-ADJOINT BOUNDARY VALUE PROBLEMS ON NETWORKS

We aim here at obtaining boundson the first nonzero eigenvalue for self-adjoint boundary valueproblems on a weighted network by means of equilibrium measures,that include the study of {sc Dirichlet, Neumann} and Mixedproblems. We also show the sharpness of these bounds throughout theanalysis of some examples. In particular we emphasize the case ofdistance-regular graphs and we show that the obtained bounds arebetter than those known until now.