A note on graphs with diameter‐preserving spanning trees

Abstract

Abstract The distance between a pair of vertices u, v in a graph G is the length of a shortest path joining u and v . The diameter diam(G) of G is the maximum distance between all pairs of vertices in G . A spanning tree T of G is diameter preserving if diam( T ) = diam( G ). In this note, we characterize graphs that have diameter‐preserving spanning trees.