Independent 2-point set domination in graphs with specified girth
A set D of vertices in a connected graph G is said to be an independent 2-point set dominating set (or in short i-2psd set) of G if D is an independent set and for every subset [Formula: see text] there exists a non-empty subset [Formula: see text] containing at most 2 vertices such that the induced...
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Taylor & Francis Group
2025-04-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2025.2488229 |
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| author | Deepti Jain |
| author_facet | Deepti Jain |
| author_sort | Deepti Jain |
| collection | DOAJ |
| description | A set D of vertices in a connected graph G is said to be an independent 2-point set dominating set (or in short i-2psd set) of G if D is an independent set and for every subset [Formula: see text] there exists a non-empty subset [Formula: see text] containing at most 2 vertices such that the induced subgraph [Formula: see text] is connected. A graph which possesses an i-2psd set is called an i-2psd graph. Every finite graph need not be an i-2psd graph; for instance [Formula: see text]. In this paper we continue to explore graphs which possess an i-2psd set and discuss i-2psd graphs with specified girth. We exhibit a relation between diameter and girth of an i-2psd graph. We characterize extremal i-2psd graphs with maximum girth, and further present a partial characterization of i-2psd graphs with girth 5. |
| format | Article |
| id | doaj-art-e27cdcd0813f45c1a06d05cb4ef0fa52 |
| institution | OA Journals |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-e27cdcd0813f45c1a06d05cb4ef0fa522025-08-20T02:24:43ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742025-04-011510.1080/09728600.2025.2488229Independent 2-point set domination in graphs with specified girthDeepti Jain0Department of Mathematics, Sri Venkateswara College, University of Delhi, Delhi, IndiaA set D of vertices in a connected graph G is said to be an independent 2-point set dominating set (or in short i-2psd set) of G if D is an independent set and for every subset [Formula: see text] there exists a non-empty subset [Formula: see text] containing at most 2 vertices such that the induced subgraph [Formula: see text] is connected. A graph which possesses an i-2psd set is called an i-2psd graph. Every finite graph need not be an i-2psd graph; for instance [Formula: see text]. In this paper we continue to explore graphs which possess an i-2psd set and discuss i-2psd graphs with specified girth. We exhibit a relation between diameter and girth of an i-2psd graph. We characterize extremal i-2psd graphs with maximum girth, and further present a partial characterization of i-2psd graphs with girth 5.https://www.tandfonline.com/doi/10.1080/09728600.2025.2488229Independent setseparable graphsGirth and circumference of graphs2-point set domination in graphsgeneralised theta graph05C69 |
| spellingShingle | Deepti Jain Independent 2-point set domination in graphs with specified girth AKCE International Journal of Graphs and Combinatorics Independent set separable graphs Girth and circumference of graphs 2-point set domination in graphs generalised theta graph 05C69 |
| title | Independent 2-point set domination in graphs with specified girth |
| title_full | Independent 2-point set domination in graphs with specified girth |
| title_fullStr | Independent 2-point set domination in graphs with specified girth |
| title_full_unstemmed | Independent 2-point set domination in graphs with specified girth |
| title_short | Independent 2-point set domination in graphs with specified girth |
| title_sort | independent 2 point set domination in graphs with specified girth |
| topic | Independent set separable graphs Girth and circumference of graphs 2-point set domination in graphs generalised theta graph 05C69 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2025.2488229 |
| work_keys_str_mv | AT deeptijain independent2pointsetdominationingraphswithspecifiedgirth |