Network topology discovery is the basis for any network management application. The problem of estimating internal structure and link-level performance from end-to-end measurements is known as network tomography. This paper proposes a novel approach to discover network characteristics, in particular, tree topology from the hop count metric (distance) between OD (Origin - Destination) pairs. The proposed method is based on Prüfer encoding and decoding techniques of trees using this metric. The method also has the potential to minimize and avoid reliance on ICMP. ©2010 IEEE.