Power Graph and Exchange Property for Resolving Sets
Usman Ali, Ghulam Abbas, Syed Ahtisham Bokhary
TL;DR
This paper presents a formula for the metric dimension of certain graphs, identifies conditions for the exchange property in resolving sets, and computes the metric dimension for power graphs of dihedral groups.
Contribution
It introduces a new formula for metric dimension, finds conditions for the exchange property, and analyzes power graphs of finite groups, including dihedral groups.
Findings
Derived a formula for metric dimension of graphs without singleton twins.
Identified sufficient conditions for the exchange property in simple graphs.
Computed the metric dimension of power graphs of dihedral groups.
Abstract
A formula for computing the metric dimension of a simple graph, having no singleton twin, is given. A sufficient condition for a simple graph to have the exchange property, for resolving sets, is found. Some families of power graphs of finite groups, having this exchange property, are identified. The metric dimension of the power graph of a dihedral group is also computed.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems