Matroids with bases as minimal resolving sets of graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912078747402240 |
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| author | Ali, Usman Hussain, Iffat Fida |
| author_facet | Ali, Usman Hussain, Iffat Fida |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matroids with bases as minimal resolving sets of graphs Ali, Usman Hussain, Iffat Fida Combinatorics Commutative Algebra Group Theory 05B35, 05C12 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. |
| title | Matroids with bases as minimal resolving sets of graphs |
| topic | Combinatorics Commutative Algebra Group Theory 05B35, 05C12 |
| url | https://arxiv.org/abs/2410.15356 |