Minimum Stretch Spanning Tree Problem in Operations on Trees

Abstract

The minimum stretch spanning tree problem for a connected graph [Formula: see text] is to find a spanning tree [Formula: see text] of [Formula: see text] such that the maximum distance in [Formula: see text] between two adjacent vertices of [Formula: see text] is minimized, where the minimum value is called the tree-stretch of [Formula: see text]. This paper presents the tree-stretch of a graph constructed by the Cartesian product of two trees. This result is a generalization of the result for the grid graphs obtained by Lin and Lin (L. Lin, Y. Lin, The minimum stretch spanning tree problem for typical graphs, Acta Mathematicae Applicatae Sinica, English Series, 37(3) (2021) 510–522). Then, we give the tree-stretch of the [Formula: see text]-th power of a tree.