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doi:10.1016/0095-8956(77)90069-7 
Copyright © 1977 Published by Elsevier Inc.
The Chartrand-Schuster conjecture: Graphs with unique distance trees are regular
Received 13 May 1974.
Available online 7 September 2004.
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Abstract
Let G be a finite connected graph with no cut vertex. A distance tree T is a spanning tree of G which further satisfies the condition that for some vertex v, dG(v, u) = dT(v, u) for all u, where dG(v, u) denotes the distance of u from v in the graph G. The conjecture that if all distance trees of G are isomorphic to each other then G is a regular graph, is settled affirmatively. The conjecture was made by Chartrand and Schuster.
