Computation of mixed resolvability for a circular ladder and its unbounded nature
Sunny Kumar Sharma, Vijay Kumar Bhat, Muhammad Azeem, Manikonda Gayathri, Bandar Almohsen, Rab Nawaz, Rab Nawaz, Rab Nawaz
TL;DR
This paper explores a specific type of graph called a pentagonal circular ladder and finds that a certain measure of its structure is unbounded.
Contribution
The paper proves that the mixed metric dimension of a pentagonal circular ladder is unbounded and depends on the number of vertices.
Findings
The mixed metric dimension of the pentagonal circular ladder is unbounded.
The mixed metric dimension depends on the number of vertices in the graph.
The mixed metric dimension is more complex than other resolvability parameters like metric and edge metric dimensions.
Abstract
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 Ph5, 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 Ph5 is unbounded, and it depends upon the number of vertices present in it. The comparison between several resolvability parameters, viz., metric dimension and edge…
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · graph theory and CDMA systems