SOME PLANAR GRAPHS WITH TEN-SIDED FACES AND THEIR METRIC DIMENSION

Let [GAMMA] = (V, E) be a non-trivial planar connected graph with vertex set V and edge set E. A set of ordered vertices R from V ([GAMMA]) is said to be a resolving set for [GAMMA] if each vertex of [GAMMA] is uniquely determined by its vector of distances to the vertices of R. The number of vertic...

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Bibliographic Details
Published in:Journal of Applied and Engineering Mathematics 2024, Vol.14 (3), p.834
Main Authors: Sharma, Sunny Kumar, Bhat, Vijay Kumar
Format: Report
Language:English
Subjects:
Analysis
Dimension theory (Topology)
Graph theory
Metric spaces
Online Access:Get full text
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Summary:Let [GAMMA] = (V, E) be a non-trivial planar connected graph with vertex set V and edge set E. A set of ordered vertices R from V ([GAMMA]) is said to be a resolving set for [GAMMA] if each vertex of [GAMMA] is uniquely determined by its vector of distances to the vertices of R. The number of vertices in a smallest resolving set is called the metric dimension of [GAMMA]. In this article, we study the metric dimension for two families of planar graphs, each of which is shown to have an independent minimum resolving set with cardinality three.
ISSN:2146-1147