In this paper, we propose an Edge Constrained Localized Delaunay graph, denoted by ECLDel, as the underlying graph for geographic routing in mobile ad hoc and sensor networks. We prove that the ECLDel is a planar t-spanner of the unit-disk graph. Geographic routing on ECLDel is as efficient as on the previous work of PLDel in terms of path length (hop count). However, the construction of ECLDel graph is far more simple and it converges faster. This is because we significantly reduce the number of messages broadcast by each node from five rounds (each round may contain several messages) to only two messages, and we define two new types of edges, the Intersecting Gabriel (IG) edges and the Unaware Intersection (UI) edges, which are constrained in the ECLDel graph. These edges help significantly reduce the size of messages broadcast by each node which reduces the communication cost, and saves the network bandwidth and node power. Our simulation results show that the average number of messages and the average size of messages broadcast by each node is, respectively, 65% and 42% less in the construction of ECLDel than that in the construction of PLDel.