On the general position number of two classes of graphs
The general position problem is to find the cardinality of the largest vertex subset SS such that no triple of vertices of SS lies on a common geodesic. For a connected graph GG, the cardinality of SS is denoted by gp(G){\rm{gp}}\left(G) and called the gp{\rm{gp}}-number (or general position number)...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-09-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0444 |
| _version_ | 1811236468231766016 |
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| author | Yao Yan He Mengya Ji Shengjin |
| author_facet | Yao Yan He Mengya Ji Shengjin |
| author_sort | Yao Yan |
| collection | DOAJ |
| description | The general position problem is to find the cardinality of the largest vertex subset SS such that no triple of vertices of SS lies on a common geodesic. For a connected graph GG, the cardinality of SS is denoted by gp(G){\rm{gp}}\left(G) and called the gp{\rm{gp}}-number (or general position number) of GG. In the paper, we obtain an upper bound and a lower bound regarding the gp{\rm{gp}}-number in all cacti with kk cycles and tt pendant edges. Furthermore, the exact value of the gp{\rm{gp}}-number on wheel graphs is determined. |
| first_indexed | 2024-04-12T12:10:20Z |
| format | Article |
| id | doaj.art-8ead94e20b5f459aa8b002405e13b81b |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-12T12:10:20Z |
| publishDate | 2022-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-8ead94e20b5f459aa8b002405e13b81b2022-12-22T03:33:36ZengDe GruyterOpen Mathematics2391-54552022-09-012011021102910.1515/math-2022-0444On the general position number of two classes of graphsYao Yan0He Mengya1Ji Shengjin2School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255000, ChinaSchool of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255000, ChinaSchool of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255000, ChinaThe general position problem is to find the cardinality of the largest vertex subset SS such that no triple of vertices of SS lies on a common geodesic. For a connected graph GG, the cardinality of SS is denoted by gp(G){\rm{gp}}\left(G) and called the gp{\rm{gp}}-number (or general position number) of GG. In the paper, we obtain an upper bound and a lower bound regarding the gp{\rm{gp}}-number in all cacti with kk cycles and tt pendant edges. Furthermore, the exact value of the gp{\rm{gp}}-number on wheel graphs is determined.https://doi.org/10.1515/math-2022-0444general position setcactuswheel05c1205c6968q25 |
| spellingShingle | Yao Yan He Mengya Ji Shengjin On the general position number of two classes of graphs Open Mathematics general position set cactus wheel 05c12 05c69 68q25 |
| title | On the general position number of two classes of graphs |
| title_full | On the general position number of two classes of graphs |
| title_fullStr | On the general position number of two classes of graphs |
| title_full_unstemmed | On the general position number of two classes of graphs |
| title_short | On the general position number of two classes of graphs |
| title_sort | on the general position number of two classes of graphs |
| topic | general position set cactus wheel 05c12 05c69 68q25 |
| url | https://doi.org/10.1515/math-2022-0444 |
| work_keys_str_mv | AT yaoyan onthegeneralpositionnumberoftwoclassesofgraphs AT hemengya onthegeneralpositionnumberoftwoclassesofgraphs AT jishengjin onthegeneralpositionnumberoftwoclassesofgraphs |