Computation of mixed resolvability for a circular ladder and its unbounded nature

• Published in: PloS one Vol. 20; no. 3; p. e0313788
• Main Authors: Sharma, Sunny Kumar, Bhat, Vijay Kumar, Azeem, Muhammad, Gayathri, Manikonda, Almohsen, Bandar
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 31.03.2025; Public Library of Science (PLoS)
• Subjects: Algorithms; Analysis; Apexes; Biology and Life Sciences; Computer and Information Sciences; Engineering and Technology; Global positioning systems; GPS; Graph theory; Graphs; Models, Theoretical; Parameter identification; Physical Sciences; Planar structures; Research methodology; Social Sciences; India
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0313788

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 P h 5 , 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 P h 5 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 P h 5 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 P h 5 .