This paper investigates the adaptive synchronization for coupled harmonic oscillators with switching topology. Edge-based adaptive control protocols are proposed for both leaderless and leader-following synchronization for coupled harmonic oscillators with switching topology. Using Lyapunov stability theory, by parting the topology graph into connected components (containing at least two connected vertices) and isolated vertex components (containing a isolated vertex), full distributed adaptive synchronization conditions are obtained, which can guarantee that the synchronization conditions do not require any global information except a mild connection assumption. Finally numerical simulations are presented to illustrate the theoretical findings. (C) 2018 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.