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arXiv · 2410.15356

Matroids with bases as minimal resolving sets of graphs

Usman Ali·Iffat Fida Hussain
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Abstract

We define an independence system associated with simple graphs. We prove that the independence system is a matroid for certain families of graphs, including trees, with bases as minimal resolving sets. Consequently, the greedy algorithm on the matroid can be used to find the minimum-cost resolving set of weighted graphs, wherein the independent system is a matroid. We also characterize hyperplanes of the matroid for trees and prove that its dual matroid is loop-free.

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Usman Ali, Iffat Fida Hussain. 2024-10-20. Matroids with bases as minimal resolving sets of graphs. https://arxiv.org/abs/2410.15356

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