Minimum tree-stretch of Hamming graphs and higher-dimensional grids

TL;DR

This paper determines the exact minimum tree stretch values for Hamming graphs and higher-dimensional grids, advancing understanding of their spanning tree properties and algorithmic complexity.

Contribution

It provides the exact tree stretch values for Hamming graphs and higher-dimensional grids, a novel contribution to graph invariants and spanning tree analysis.

Findings

Exact tree stretch values for Hamming graphs obtained

Exact tree stretch values for higher-dimensional grids obtained

Enhances understanding of spanning tree properties in complex graphs

Abstract

The minimum stretch spaning tree problem for a grah G is to find a spaning tree T of G such as that the maximum distance in T between two adjacent vertices is minimized. The minimum value of this optimization problem gives rise to a grpah invariant {\sigma} T(G) called the tree stretch of G. The problem has been studied in the algorithmic aspects, such as NP-hardness and fixed-parameter solvability. This paper presents the exact values {\sigma} T(G) of hamming graphs Kn1 * Kn2 * ... * Knd and the higer-dimensional grids Pn1 * Pn2 * ... * Pnd.