Computing closeness for some graphs
The analysis of networks involves several crucial parameters. In this paper, we consider the closeness parameter, which is based on the total distance between every pair of vertices. Initially, we delve into a discussion about the applicability of the closeness parameter to Mycielski graphs. Our fin...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2023-12-01
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| Series: | Acta Universitatis Sapientiae: Informatica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/ausi-2023-0015 |
| _version_ | 1797387248602185728 |
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| author | Tunçel Gölpek Hande Aytaç Aysun |
| author_facet | Tunçel Gölpek Hande Aytaç Aysun |
| author_sort | Tunçel Gölpek Hande |
| collection | DOAJ |
| description | The analysis of networks involves several crucial parameters. In this paper, we consider the closeness parameter, which is based on the total distance between every pair of vertices. Initially, we delve into a discussion about the applicability of the closeness parameter to Mycielski graphs. Our findings are categorized based on the underlying graph’s diameter. The formula for calculating the closeness of a Mycielski graph is derived for graphs with a diameter of less than or equal to 4. Furthermore, we establish a sharp lower bound for the closeness of a Mycielski graph when the diameter of the underlying graph is greater than 4. To achieve this, the closeness of the Mycielski transformation of a path graph plays an important role. Additionally, leveraging the obtained results, we examine the closeness of a special planar construction composed of path and cycle graphs, as well as its Mycielski transformation. |
| first_indexed | 2024-03-08T22:21:08Z |
| format | Article |
| id | doaj.art-50fd694770334c6a9496e0357c0f7918 |
| institution | Directory Open Access Journal |
| issn | 2066-7760 |
| language | English |
| last_indexed | 2024-03-08T22:21:08Z |
| publishDate | 2023-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Acta Universitatis Sapientiae: Informatica |
| spelling | doaj.art-50fd694770334c6a9496e0357c0f79182023-12-18T12:44:44ZengSciendoActa Universitatis Sapientiae: Informatica2066-77602023-12-0115222123810.2478/ausi-2023-0015Computing closeness for some graphsTunçel Gölpek Hande0Aytaç Aysun11Dokuz Eylul University Maritime Faculty Buca Izmir, Turkey2Ege University, Department of MathematicsBornova Izmir, TurkeyThe analysis of networks involves several crucial parameters. In this paper, we consider the closeness parameter, which is based on the total distance between every pair of vertices. Initially, we delve into a discussion about the applicability of the closeness parameter to Mycielski graphs. Our findings are categorized based on the underlying graph’s diameter. The formula for calculating the closeness of a Mycielski graph is derived for graphs with a diameter of less than or equal to 4. Furthermore, we establish a sharp lower bound for the closeness of a Mycielski graph when the diameter of the underlying graph is greater than 4. To achieve this, the closeness of the Mycielski transformation of a path graph plays an important role. Additionally, leveraging the obtained results, we examine the closeness of a special planar construction composed of path and cycle graphs, as well as its Mycielski transformation.https://doi.org/10.2478/ausi-2023-0015graph vulnerabilityclosenessmycielski graphtadpole graph |
| spellingShingle | Tunçel Gölpek Hande Aytaç Aysun Computing closeness for some graphs Acta Universitatis Sapientiae: Informatica graph vulnerability closeness mycielski graph tadpole graph |
| title | Computing closeness for some graphs |
| title_full | Computing closeness for some graphs |
| title_fullStr | Computing closeness for some graphs |
| title_full_unstemmed | Computing closeness for some graphs |
| title_short | Computing closeness for some graphs |
| title_sort | computing closeness for some graphs |
| topic | graph vulnerability closeness mycielski graph tadpole graph |
| url | https://doi.org/10.2478/ausi-2023-0015 |
| work_keys_str_mv | AT tuncelgolpekhande computingclosenessforsomegraphs AT aytacaysun computingclosenessforsomegraphs |