  The high-level contribution of this paper is to establish benchmarks for the
minimum hop count per source-receiver path and the minimum number of edges per
tree for multicast routing in mobile ad hoc networks (MANETs) under different
mobility models. In this pursuit, we explore the tradeoffs between these two
routing strategies with respect to hop count, number of edges and lifetime per
multicast tree with respect to the Random Waypoint, City Section and Manhattan
mobility models. We employ the Breadth First Search algorithm and the Minimum
Steiner Tree heuristic for determining a sequence of minimum hop and minimum
edge trees respectively. While both the minimum hop and minimum edge trees
exist for a relatively longer time under the Manhattan mobility model; the
number of edges per tree and the hop count per source-receiver path are
relatively low under the Random Waypoint model. For all the three mobility
models, the minimum edge trees have a longer lifetime compared to the minimum
hop trees and the difference in lifetime increases with increase in network
density and/or the multicast group size. Multicast trees determined under the
City Section model incur fewer edges and lower hop count compared to the
Manhattan mobility model.
