Dispersed graph labellings
William J. Martin, Douglas R. Stinson

TL;DR
This paper investigates the maximum dispersion in graph labellings, providing bounds, exact values for specific graph classes, and new construction methods, despite the NP-hardness of the problem.
Contribution
It introduces bounds, exact values for key graphs, and novel construction techniques for dispersed graph labellings, advancing understanding of this NP-hard problem.
Findings
Exact $DL(G)$ for cycles, paths, grids, hypercubes, and binary trees.
Established degree-based bounds and product constructions.
Proved NP-hardness of computing $DL(G)$.
Abstract
A -dispersed labelling of a graph on vertices is a labelling of the vertices of by the integers such that for . denotes the maximum value of such that has a -dispersed labelling. In this paper, we study upper and lower bounds on . Computing is NP-hard. However, we determine the exact values of for cycles, paths, grids, hypercubes and complete binary trees. We also give a product construction and we prove a degree-based bound.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Advanced Graph Theory Research
