1. Distance Approximating Trees in Graphs
A strongly chordal graph and an additive tree 3-spanner of it, produced by our algorithm. This graph has no additive tree 2-spanner.

2. Distance Approximating Trees in Graphs
Case (it is allowed to use new edges) distance -approximating trees
A tree T=(V,E’) is a distance –approximating tree of a graph G=(V,E) if
for any

3. Distance Approximating Trees in Graphs Distance -approximating trees
Problem: Given G and integer , decide whether G has a distance -approximating tree.
Our results ( is the length of a longest chordless simple cycle in G)
Applications
Given a chordal graph G. After linear time preprocessing, for any two vertices of G, the distance with an error at most 2 can be computed in only O(1) time.
Efficient approximate solutions of several NP-complete problems related to distances.