On Symmetrical Convex Polytopes and their Edge Resolvability
Document Type
Article
Publication Title
Journal of Combinatorial Mathematics and Combinatorial Computing
Abstract
The metric dimension of a graph Γ = (V, E), denoted by dim(Γ), is the least cardinality of a set of vertices in Γ such that each vertex in Γ is determined uniquely by its vector of distance to the vertices of the chosen set. The topological distance between an edge ε = yz ∈ E and a vertex k ∈ V is defined as d(ε, k) = min{d(z, k), d(y, k)}. A subset of vertices RΓ in V is called an edge resolving set for Γ if for each pair of different edges e1 and e2 in E, there is a vertex j ∈ RΓ implying d(e1, j), d(e2, j). An edge resolving set with minimum cardinality is called the edge metric basis for Γ and this cardinality is the edge metric dimension of Γ, denoted by dimE(Γ). In this article, we show that the cardinality of minimum edge resolving set is three or four, for two classes of convex polytopes (Sn and Tn, exist in the literature).
First Page
229
Last Page
242
DOI
10.61091/jcmcc122-19
Publication Date
1-1-2024
Recommended Citation
Sharma, Sunny Kumar and Bhat, Vijay Kumar, "On Symmetrical Convex Polytopes and their Edge Resolvability" (2024). Open Access archive. 10610.
https://impressions.manipal.edu/open-access-archive/10610
