Domination on cactus chains of pentagons
Introduction/purpose: A graph as a mathematical object occupies a special place in science. Graph theory is increasingly used in many spheres of business and scientific fields. This paper analyzes pentagonal cactus chains, a special type of graphs composed of pentagonal cycles in which two adjac...
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| Format: | Article |
| Language: | English |
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University of Defence in Belgrade
2022-07-01
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| Series: | Vojnotehnički Glasnik |
| Subjects: | |
| Online Access: | https://scindeks.ceon.rs/article.aspx?artid=0042-84692203583M |
| _version_ | 1818531684855840768 |
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| author | Miroslava Mihajlov Carević |
| author_facet | Miroslava Mihajlov Carević |
| author_sort | Miroslava Mihajlov Carević |
| collection | DOAJ |
| description | Introduction/purpose: A graph as a mathematical object occupies a special
place in science. Graph theory is increasingly used in many spheres of
business and scientific fields. This paper analyzes pentagonal cactus
chains, a special type of graphs composed of pentagonal cycles in which
two adjacent cycles have only one node in common. The aim of the
research is to determine the dominant set and the dominance number on
ortho and meta pentagonal cactus chains.
Methods: When the corresponding destinations are treated as graph nodes
and the connections between them as branches in the graph, the complete
structure of the graph is obtained, to which the laws of graph theory are
applied. The vertices of the pentagon are treated as nodes of the graph and
the sides as branches in the graph. By applying mathematical methods, the
dominance was determined on one pentagon, then on two pentagons with
a common node, and then on ortho and meta pentagonal cactus chains.
Results: The research has shown that the dominance number on the ortho
chain 𝑂ℎ of the length h ≥ 2 is equal to the value of the expression ⌈3ℎ/2⌉ while
on the meta chain 𝑀ℎ it is equal to the value of the expression h+1, which
was proven in this paper.
Conclusion: The results show that the dominant sets and the dominance
numbers on ortho and meta pentagonal cactus chains are determined and
explicitly expressed by mathematical expressions. They also point to the
possibility of their application in the fields of science as well as in the
spheres of business in which these structures appear. |
| first_indexed | 2024-12-11T17:35:40Z |
| format | Article |
| id | doaj.art-5e0ded0ccc704cbaae1a93a769394160 |
| institution | Directory Open Access Journal |
| issn | 0042-8469 2217-4753 |
| language | English |
| last_indexed | 2024-12-11T17:35:40Z |
| publishDate | 2022-07-01 |
| publisher | University of Defence in Belgrade |
| record_format | Article |
| series | Vojnotehnički Glasnik |
| spelling | doaj.art-5e0ded0ccc704cbaae1a93a7693941602022-12-22T00:56:41ZengUniversity of Defence in BelgradeVojnotehnički Glasnik0042-84692217-47532022-07-0170358359710.5937/vojtehg70-36576Domination on cactus chains of pentagonsMiroslava Mihajlov Carević0https://orcid.org/0000-0001-6458-2044Faculty for Business, Economics and Entrepeneurship, Belgrade, Republic of SerbiaIntroduction/purpose: A graph as a mathematical object occupies a special place in science. Graph theory is increasingly used in many spheres of business and scientific fields. This paper analyzes pentagonal cactus chains, a special type of graphs composed of pentagonal cycles in which two adjacent cycles have only one node in common. The aim of the research is to determine the dominant set and the dominance number on ortho and meta pentagonal cactus chains. Methods: When the corresponding destinations are treated as graph nodes and the connections between them as branches in the graph, the complete structure of the graph is obtained, to which the laws of graph theory are applied. The vertices of the pentagon are treated as nodes of the graph and the sides as branches in the graph. By applying mathematical methods, the dominance was determined on one pentagon, then on two pentagons with a common node, and then on ortho and meta pentagonal cactus chains. Results: The research has shown that the dominance number on the ortho chain 𝑂ℎ of the length h ≥ 2 is equal to the value of the expression ⌈3ℎ/2⌉ while on the meta chain 𝑀ℎ it is equal to the value of the expression h+1, which was proven in this paper. Conclusion: The results show that the dominant sets and the dominance numbers on ortho and meta pentagonal cactus chains are determined and explicitly expressed by mathematical expressions. They also point to the possibility of their application in the fields of science as well as in the spheres of business in which these structures appear.https://scindeks.ceon.rs/article.aspx?artid=0042-84692203583Mgraphpentagonal cactus-chaindominant setdominance number |
| spellingShingle | Miroslava Mihajlov Carević Domination on cactus chains of pentagons Vojnotehnički Glasnik graph pentagonal cactus-chain dominant set dominance number |
| title | Domination on cactus chains of pentagons |
| title_full | Domination on cactus chains of pentagons |
| title_fullStr | Domination on cactus chains of pentagons |
| title_full_unstemmed | Domination on cactus chains of pentagons |
| title_short | Domination on cactus chains of pentagons |
| title_sort | domination on cactus chains of pentagons |
| topic | graph pentagonal cactus-chain dominant set dominance number |
| url | https://scindeks.ceon.rs/article.aspx?artid=0042-84692203583M |
| work_keys_str_mv | AT miroslavamihajlovcarevic dominationoncactuschainsofpentagons |