Computation of mixed resolvability for a circular ladder and its unbounded nature.
Let Γ = Γ(V ,E) be a simple, planar, connected, and undirected graph. The article primarily concentrates on a category of planar graphs, detailing the explicit identification of each member within this graph family. Within the domain of graph theory, the parameters used to uniquely identify vertices...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2025-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0313788 |
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| author | Sunny Kumar Sharma Vijay Kumar Bhat Muhammad Azeem Manikonda Gayathri Bandar Almohsen |
| author_facet | Sunny Kumar Sharma Vijay Kumar Bhat Muhammad Azeem Manikonda Gayathri Bandar Almohsen |
| author_sort | Sunny Kumar Sharma |
| collection | DOAJ |
| description | Let Γ = Γ(V ,E) be a simple, planar, connected, and undirected graph. The article primarily concentrates on a category of planar graphs, detailing the explicit identification of each member within this graph family. Within the domain of graph theory, the parameters used to uniquely identify vertices and edges of a graph are commonly referred to as variants of metric dimension, collectively known as resolvability parameters. The present study focuses on the intricate planar structure of a five-sided circular ladder (pentagonal); denoted by [Formula: see text] and investigate some of the recently introduced resolvability parameters for it, which are mixed metric basis and mixed metric dimension. We prove that the mixed metric dimension for [Formula: see text] is unbounded, and it depends upon the number of vertices present in it. The comparison between several resolvability parameters, viz., metric dimension and edge metric dimension, for [Formula: see text] with mixed metric dimension have also been incorporated in this manuscript, indicating higher level of complexity for resolving both edge and vertex-based relationships. Moreover, several theoretical as well as application based properties, including examples, have also been discussed for [Formula: see text]. |
| format | Article |
| id | doaj-art-751df47c90354d858c6f02cc4d85a4c0 |
| institution | OA Journals |
| issn | 1932-6203 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-751df47c90354d858c6f02cc4d85a4c02025-08-20T02:08:26ZengPublic Library of Science (PLoS)PLoS ONE1932-62032025-01-01203e031378810.1371/journal.pone.0313788Computation of mixed resolvability for a circular ladder and its unbounded nature.Sunny Kumar SharmaVijay Kumar BhatMuhammad AzeemManikonda GayathriBandar AlmohsenLet Γ = Γ(V ,E) be a simple, planar, connected, and undirected graph. The article primarily concentrates on a category of planar graphs, detailing the explicit identification of each member within this graph family. Within the domain of graph theory, the parameters used to uniquely identify vertices and edges of a graph are commonly referred to as variants of metric dimension, collectively known as resolvability parameters. The present study focuses on the intricate planar structure of a five-sided circular ladder (pentagonal); denoted by [Formula: see text] and investigate some of the recently introduced resolvability parameters for it, which are mixed metric basis and mixed metric dimension. We prove that the mixed metric dimension for [Formula: see text] is unbounded, and it depends upon the number of vertices present in it. The comparison between several resolvability parameters, viz., metric dimension and edge metric dimension, for [Formula: see text] with mixed metric dimension have also been incorporated in this manuscript, indicating higher level of complexity for resolving both edge and vertex-based relationships. Moreover, several theoretical as well as application based properties, including examples, have also been discussed for [Formula: see text].https://doi.org/10.1371/journal.pone.0313788 |
| spellingShingle | Sunny Kumar Sharma Vijay Kumar Bhat Muhammad Azeem Manikonda Gayathri Bandar Almohsen Computation of mixed resolvability for a circular ladder and its unbounded nature. PLoS ONE |
| title | Computation of mixed resolvability for a circular ladder and its unbounded nature. |
| title_full | Computation of mixed resolvability for a circular ladder and its unbounded nature. |
| title_fullStr | Computation of mixed resolvability for a circular ladder and its unbounded nature. |
| title_full_unstemmed | Computation of mixed resolvability for a circular ladder and its unbounded nature. |
| title_short | Computation of mixed resolvability for a circular ladder and its unbounded nature. |
| title_sort | computation of mixed resolvability for a circular ladder and its unbounded nature |
| url | https://doi.org/10.1371/journal.pone.0313788 |
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