The Vertex Strong Geodetic Number of a Graph

Article Sidebar

PDF
Published: Nov 23, 2023
DOI: https://doi.org/10.53555/jrtdd.v6i10s.2752
Keywords:
strong geodetic number vertex strong geodetic number geodetic number.

Main Article Content

C. Saritha
T. Muthu Nesa Beula

Abstract

Let  be a vertex of  and . Then for each vertex  . Let  be a selected fixed shortest - path. Then we set  and let . If  for some then the set  is called a vertex strong geodetic set of  The minimum cardinality of a vertex strong geodetic set of  is called the vertex strong geodetic number of  and is denoted by  Some of the standard graphs are determined. Necessary conditions for  to be   is given for some vertex  in . It is shown for every pair of integers  and  with  there exists a connected graph  such that  and  for some  in

Article Details

How to Cite
C. Saritha, & T. Muthu Nesa Beula. (2023). The Vertex Strong Geodetic Number of a Graph. Journal for ReAttach Therapy and Developmental Diversities, 6(10s), 2075–2081. https://doi.org/10.53555/jrtdd.v6i10s.2752
Issue
Vol. 6 No. 10s (2023)
Section
Articles
Author Biographies

C. Saritha

Register Number 20123182092003, Research Scholar, Department of Mathematics, Women’s Christian College, Nagercoil - 629 001, Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627 012, Tamil Nadu, India. 

T. Muthu Nesa Beula

Assistant Professor, Department of Mathematics, Women’s Christian College, Nagercoil - 629 001, Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627 012, Tamil Nadu, India. 

References

F. Buckley and F. Harary, Distance in Graphs, Addison-Wesley, Redwood City, CA, 1990.

L. G. Bino Infanta and D. Antony Xavier, Strong upper geodetic number of graphs, Communications in Mathematics and Applications 12(3), 2021, 737–748.

G. Chartrand and P. Zhang, The forcing geodetic number of a graph, Discuss. Math. Graph Theory, 19, 1999, 45-58.

G. Chartrand, F. Harary and P. Zhang, On the geodetic number of a graph, Networks, 39, 2002, 1-6.

V. Gledel, V. Irsic, and S. Klavzar, Strong geodetic cores and cartesian product graphs, arXiv:1803.11423 [math.CO] (30 Mar 2018).

Huifen Ge, Zao Wang-and Jinyu Zou Strong geodetic number in some networks, Journal of Mathematical Resarch-11(2), 2019, 20-29.

V. Irsic, Strong geodetic number of complete bipartite graphs and of graphs with specified diameter, Graphs and Combin. 34, 2018, 443–456.

V. Irsic, and S. Klavzar, Strong geodetic problem on Cartesian products of graphs, RAIRO Oper. Res. 52, 2018, 205–216.

P. Manuel, S. Klavzar, A. Xavier, A. Arokiaraj, and E. Thomas, Strong edge geodetic problem in networks, Open Math. 15, 2017, 1225–1235.

A. P. Santhakumaran and P. Titus, Vertex Geodomination in Graphs, Bulletin of Kerala Mathematics Association 2 (2), 2005, 45 – 57.

C.Saritha and T.Muthu Nesa Beula, The forcing strong geodetic number of a graph, proceedings of the International conference on Advances and Applications in Mathematical Sciences, 2022,76-80.