Research Article
Metric Dimension of Graphs and its Application to Robotic Navigation
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 184 - Issue 15 |
| Published: Jun 2022 |
| Authors: Basma Mohamed |
10.5120/ijca2022922090
|
Basma Mohamed . Metric Dimension of Graphs and its Application to Robotic Navigation. International Journal of Computer Applications. 184, 15 (Jun 2022), 1-3. DOI=10.5120/ijca2022922090
@article{ 10.5120/ijca2022922090,
author = { Basma Mohamed },
title = { Metric Dimension of Graphs and its Application to Robotic Navigation },
journal = { International Journal of Computer Applications },
year = { 2022 },
volume = { 184 },
number = { 15 },
pages = { 1-3 },
doi = { 10.5120/ijca2022922090 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2022
%A Basma Mohamed
%T Metric Dimension of Graphs and its Application to Robotic Navigation%T
%J International Journal of Computer Applications
%V 184
%N 15
%P 1-3
%R 10.5120/ijca2022922090
%I Foundation of Computer Science (FCS), NY, USA
Abstract
Metric dimension of graphs has several applications to networking such as network navigation, network discovery and verification, wireless sensor network localization, and locating intruders in a network. This paper investigates the metric dimension in terms of contraction and bijection when a robot is navigating a network modeled by the(2,1)C4-snake graph, 2∆2–snake graph and 3C4–snake graph.
References
- P. J. Slater. Leaves of trees. 1975. In: Proc. 6th Southeastern Conf. on Combinatorics, Graph theory andComputing.
- Harary, F. and Melter, R. A. 1976. On the metric dimension of a graph. Arscombinatorica.
- Javaid, I. Rahim, M. T. and Ali, K. 2008. Families of regular graphs with constant metric dimension. Utilitasmathematica.
- Khuller, S., Raghavachari, B. and Rosenfeld,A.1996. Landmarks in graphs. Discreteapplied mathematics.
- Gary, M.R. and Johnson, D.S. 1979. Computers and Intractability: A Guide to the Theory of NP-completeness.
- Melter, R.A. and Tomescu, I. 1984. Metric bases in digital geometry. Computer vision, graphics, and image Processing.
- Hernando, C., Mora, M., Pelayo, I.M., Seara, C. Cáceres, J. and Puertas, M.L. 2005. On the metric dimension of some families of graphs. Electronic notes in discrete mathematics.
- Chartrand, G., Eroh, L., Johnson, M.A. and Oellermann, O.R. 2000. Resolvability in graphs and the metric dimension of a graph. Discrete applied mathematics.
- Poisson, C. and Zhang, P. 2002. The metric dimension of unicyclic graphs. Journal of combinatorial mathematics and combinatorial computing.
- Sooryanarayana, B. and Shanmukha, B. 2001. A note on
- metric dimension. Far East J. Appl. Math.
- Sooryanaranyana, B. and Shanmuka, B. 2002. Metric dimension of a wheel. Far. East journal of applied mathematics.
- Susilowati, L., Zahidah, S., Nastiti, R.D. and Utoyo, M.I. 2020. The metric dimension of k-subdivision graphs. In Journal of Physics: Conference Series. IOP Publishing.
- Imran, S., Siddiqui, M.K., Imran, M. and Hussain, M. 2018. On metric dimensions of symmetric graphs obtained by rooted product. Mathematics.
- Bailey, R.F. and Cameron, P.J. 2011. Base size, metric dimension and other invariants of groups and graphs. Bulletin of the london mathematical society.
- Manjusha, R. and Kuriakose, A.S. 2015. Metric dimension and uncertainty of traversing robots in anetwork. International journal on applications of graph theory in wireless ad hoc networks and sensor networks (GRAPH-HOC).
- Beerliova, Z., Eberhard, F., Erlebach, T., Hall,A., Hoffmann, M., Mihal'ak, M., & Ram, L. S. (2006). Network discovery and verification. IEEE Journal on selected areas in communications, 24(12), 2168-2181.
Index Terms
Keywords