Barycentric Subdivision of Cayley Graphs With Constant Edge Metric Dimension

A motion of a robot in space is represented by a graph. A robot change its position from point to point and its position can be determined itself by distinct labelled landmarks points. The problem is to determine the minimum number of landmarks to find the unique position of the robot, this phenomen...

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Bibliographic Details
Published in:IEEE access 2020, Vol.8, p.80624-80628
Main Authors: Koam, Ali N. A., Ahmad, Ali
Format: Article
Language:English
Subjects:
Apexes
barycentric subdivision
Cayley graph
edge metric dimension
Generators
Graph theory
Graphical representations
Graphs
Landmarks
Mathematics
Measurement
Metric dimension
Object recognition
resolving set
Robot dynamics
Robot sensing systems
Robots
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Summary:A motion of a robot in space is represented by a graph. A robot change its position from point to point and its position can be determined itself by distinct labelled landmarks points. The problem is to determine the minimum number of landmarks to find the unique position of the robot, this phenomena is known as metric dimension. Motivated by this a new modification was introduced by Kelenc. In this paper, we computed the edge metric dimension of barycentric subdivision of Cayley graphs Cay(Z α ⊕Z β ), for every α ≥ 6, β ≥ 2 and an observation is made that it has constant edge metric dimension and only three carefully chosen vertices can appropriately suffice to resolve all the edges of barycentric subdivision of Cayley graphs Cay(Z α ⊕ Z β ).
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2020.2990109