A Study on the Strong Metric Dimension Problem for Certain Tree-Derived Networks | Chapter 6 | Mathematics and Computer Science: Research Updates Vol. 5

The concept of metric dimension is a well-known graph invariant with numerous practical applications, particularly in areas such as network navigation, robot navigation, chemistry, and image processing. One of its notable uses is in designing efficient navigation systems within transportation and communication networks, where uniquely identifying every location through minimal reference points is critical. The strong metric dimension is another invariant that is more restricted than the metric dimension. This study examines the strong metric dimension problem in a class of tree-derived networks.

 

Author (s) Details

Prathab H
P.G & Research Department of Mathematics, Pachaiyappa’s College, Chennai 600030, India and Department of Mathematics, Saveetha Engineering College, Chennai, India.

Chandrasekarn S
P.G & Research Department of Mathematics, Pachaiyappa’s College, Chennai 600030, India.

 

Sathish K
Department of Mathematics and Statistics, Faculty of Science and Humanities, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v5/5344

Metric Dimension of Flower Graphs | Chapter 37 | Innovative Solutions: A Systematic Approach towards Sustainable Future

The metric dimension of a connected graph G is the smallest number of nodes (resolving set) required to identify all other nodes based on shortest path distances uniquely. The notion of resolving set is significant in robotic navigation and to construct various plan of action for the mastermind game.A resolving set of G is a set \(S\subset V (G)\) if some vertices of S resolve every pair of nodes u and v of G. A metric basis represents the lowest number of nodes in a resolving set. In this research article we characterize the metric dimension and distance matrix of sunflower graphs and flower snarks.

 

Author (s) Details

 

Girisha A
Department of Mathematics, Acharya Institute of Technology, Bengaluru, India.

 

P Rajendra
Department of Mathematics, CMR Institute of Technology, Bengaluru, India.

 

Pushpa S
Department of Mathematics, SJB Institute of Technology, Bengaluru, India.

 

Ramya R
Department of Computer Science Engineering, Sapthagiri NPS University, Bengaluru, India.

 

Shashidhar Shekar N
Department of Mathematics, KLE technological University, Dr. M S Sheshgiri Campus, Belagavi, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mono/978-93-49238-47-3/CH37