Abstract
Abstract The minimum stretch spanning tree problem for a graph G is to find a spanning tree T of G such that the maximum distance in T between two adjacent vertices of G is minimized, where the minimum value is called the tree-stretchof G. There has been extensive study on the algorithmic aspects, such as the NP-hardness and fixed-parameter solvability. We are concerned in this paper with the computation of exact tree-stretch for given graph families. We relate an optimization approach of computing lower and upper bounds. This approach is applied to several typical graph families, such as the hypercubes Qn, the graph products Km × Kn, Pm × Kn, Cm × Cn, Pm × Cn, Pm × Pn, and Km × Cn.
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