2024/10/11 by S. Prabhu, Prabhu, S., D. Sagaya Rani Jeba +5 · 1 citation
Computer Science · Mathematics · #05C12 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2410.08662
openalex publication_date 2024/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The metric dimension of a graph measures how uniquely vertices may be identified using a set of landmark vertices. This concept is frequently used in the study of network architecture, location-based problems and communication. Given a graph G, the metric dimension, denoted as dim(G), is the minimum size of a resolving set, a subset of vertices such that for every pair of vertices in G, there exists a vertex in the resolving set whose shortest path distance to the two vertices is different. This subset of vertices helps to uniquely determine the location of other vertices in the graph. A basis is a resolving set with a least cardinality. Finding a basis is a problem with practical applications in network design, where it is important to efficiently locate and identify nodes based on a limited set of reference points. The Cartesian product of Pm and Pn is the grid network in network science. In this paper, we investigate two novel types of grids in network science: the Villarceau grid Type I and Type II. For each of these grid types, we find the precise metric dimension.