Bounds on the Partition Dimension of Convex Polytopes
Copyright© Bentham Science Publishers; For any queries, please email at epubbenthamscience.net..
AIMS AND OBJECTIVE: The idea of partition and resolving sets play an important role in various areas of engineering, chemistry and computer science such as robot navigation, facility location, pharmaceutical chemistry, combinatorial optimization, networking, and mastermind game.
METHODS: In a graph, to obtain the exact location of a required vertex, which is unique from all the vertices, several vertices are selected; this is called resolving set, and its generalization is called resolving partition, where selected vertices are in the form of subsets. A minimum number of partitions of the vertices into sets is called partition dimension.
RESULTS: It was proved that determining the partition dimension of a graph is a nondeterministic polynomial time (NP) problem. In this article, we find the partition dimension of convex polytopes and provide their bounds.
CONCLUSION: The major contribution of this article is that due to the complexity of computing the exact partition dimension, we provide the bounds and show that all the graphs discussed in the results have partition dimensions either less or equals to 4, but not greater than 4.
| Medienart: |
E-Artikel |
|---|
| Erscheinungsjahr: |
2022 |
|---|---|
| Erschienen: |
2022 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:25 |
|---|---|
| Enthalten in: |
Combinatorial chemistry & high throughput screening - 25(2022), 3 vom: 25., Seite 547-553 |
| Sprache: |
Englisch |
|---|
| Beteiligte Personen: |
Liu, Jia-Bao [VerfasserIn] |
|---|
| Links: |
|---|
| Themen: |
Bounded partition dimension. |
|---|
| Anmerkungen: |
Date Completed 22.03.2022 Date Revised 22.03.2022 published: Print Citation Status MEDLINE |
|---|
| doi: |
10.2174/1386207323666201204144422 |
|---|
| funding: |
|
|---|---|
| Förderinstitution / Projekttitel: |
|
| PPN (Katalog-ID): |
NLM318464780 |
|---|
| LEADER | 01000naa a22002652 4500 | ||
|---|---|---|---|
| 001 | NLM318464780 | ||
| 003 | DE-627 | ||
| 005 | 20231225165416.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 231225s2022 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.2174/1386207323666201204144422 |2 doi | |
| 028 | 5 | 2 | |a pubmed24n1061.xml |
| 035 | |a (DE-627)NLM318464780 | ||
| 035 | |a (NLM)33280591 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 100 | 1 | |a Liu, Jia-Bao |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Bounds on the Partition Dimension of Convex Polytopes |
| 264 | 1 | |c 2022 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ƒaComputermedien |b c |2 rdamedia | ||
| 338 | |a ƒa Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Date Completed 22.03.2022 | ||
| 500 | |a Date Revised 22.03.2022 | ||
| 500 | |a published: Print | ||
| 500 | |a Citation Status MEDLINE | ||
| 520 | |a Copyright© Bentham Science Publishers; For any queries, please email at epubbenthamscience.net. | ||
| 520 | |a AIMS AND OBJECTIVE: The idea of partition and resolving sets play an important role in various areas of engineering, chemistry and computer science such as robot navigation, facility location, pharmaceutical chemistry, combinatorial optimization, networking, and mastermind game | ||
| 520 | |a METHODS: In a graph, to obtain the exact location of a required vertex, which is unique from all the vertices, several vertices are selected; this is called resolving set, and its generalization is called resolving partition, where selected vertices are in the form of subsets. A minimum number of partitions of the vertices into sets is called partition dimension | ||
| 520 | |a RESULTS: It was proved that determining the partition dimension of a graph is a nondeterministic polynomial time (NP) problem. In this article, we find the partition dimension of convex polytopes and provide their bounds | ||
| 520 | |a CONCLUSION: The major contribution of this article is that due to the complexity of computing the exact partition dimension, we provide the bounds and show that all the graphs discussed in the results have partition dimensions either less or equals to 4, but not greater than 4 | ||
| 650 | 4 | |a Journal Article | |
| 650 | 4 | |a Research Support, Non-U.S. Gov't | |
| 650 | 4 | |a Partition dimension | |
| 650 | 4 | |a bounded partition dimension. | |
| 650 | 4 | |a convex polytopes | |
| 650 | 4 | |a resolving partition | |
| 650 | 4 | |a resolving sets | |
| 700 | 1 | |a Nadeem, Muhammad Faisal |e verfasserin |4 aut | |
| 700 | 1 | |a Azeem, Mohammad |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Combinatorial chemistry & high throughput screening |d 1998 |g 25(2022), 3 vom: 25., Seite 547-553 |w (DE-627)NLM097489352 |x 1875-5402 |7 nnns |
| 773 | 1 | 8 | |g volume:25 |g year:2022 |g number:3 |g day:25 |g pages:547-553 |
| 856 | 4 | 0 | |u http://dx.doi.org/10.2174/1386207323666201204144422 |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a GBV_NLM | ||
| 951 | |a AR | ||
| 952 | |d 25 |j 2022 |e 3 |b 25 |h 547-553 | ||