Changing and Unchanging the Geodetic Number: Edge Removal
DOI:
https://doi.org/10.12723/mjs.67.8Keywords:
Geodesic set, Geodetic numberAbstract
Let S be a collection of elements in a vertex set V. If every vertex in a graph G falls on a geodesic connecting two vertices from S, then that graph is said to be a geodesic set. g(G) is the smallest cardinality of the geodesic subset of a graph G is known as the geodetic number. This study investigates how the removal of an edge affects some unique families of graphs' geodetic numbers.
References
F. Buckley, F. Harary, Distance in Graphs, Addition-Wesley, 1990.
F. Buckley, F. Harary, L.V. Quintas, Extremal Results on the Geodetic Number of a Graph, Scientia (1988) 17–26.
G. Chartrand, F. Harary, P. Zhang, Geodetic Sets in Graphs, Discussions Mathematicae Graph Theory. 20 (2000) 129 – 138.
G. Chartrand, Lesniak, Graphs and Digraphs, CRC press, 2005.
G. Chartrand, F. Harary, P. Zhang, On the Geodetic Number of a Graph, Networks. 39(1), (2002) 1 – 6.
F. Harary, E. Loukakis, C. Tsouros. The Geodetic Number of a Graph, Math. Comput. Modeling. 17, (1993) 89 – 95.
G. Micheal Antony, R. Arul Ananthan, S. Balamurugan, The Geodetic Number of Some Special Graphs, International Conf. on Advanced Research in Mathematical Sci. Conf. Proceedings, 2021.
G. Micheal Antony, R. Arul Ananthan, S. Balamurugan, The Geodetic Number of Some Special Graphs, International Conf. on Advanced Mathematical Modeling And Computational Techniques Conf. Proceedings, 2021.
S. Balamurugan, G. Micheal Antony, Criticality and Stability of the Geodesic number in Graphs (Communicated).
Additional Files
Published
Issue
Section
License
Copyright (c) 2024 G Micheal Antony Gnana santhiyagu, Dr.S Balamurugan, R Arul Ananthan
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
