Strong Upper Geodetic Number of Graphs

Authors

  • L. G. Bino Infanta Department of Mathematics, Loyola College (University of Madras), Chennai, India https://orcid.org/0000-0003-1629-2792
  • D. Antony Xavier Department of Mathematics, Loyola College (University of Madras), Chennai, India

DOI:

https://doi.org/10.26713/cma.v12i3.1597

Keywords:

Geodetic set, Strong geodetic set, Upper geodetic number.

Abstract

Let \(G=(V,E)\) be a graph. A set \(S\in G\) is a strong geodetic set, if each vertex \(v\in G/S\) lies on a fixed geodetic between the pair of vertices of \(S\). A set \(S\) is called a minimal strong geodetic set, if no proper subset of \(S\) is a strong geodetic set. The maximum cardinality of a minimal strong geodetic set is the strong upper geodetic number. It is denoted by \(sg^+(G)\). In this paper, we have proved the NP-completeness of strong upper geodetic number. Some results on strong upper geodetic number and strong upper edge geodetic number of graphs were also found.

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References

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Published

30-09-2021
CITATION

How to Cite

Infanta, L. G. B., & Xavier, D. A. (2021). Strong Upper Geodetic Number of Graphs. Communications in Mathematics and Applications, 12(3), 737–748. https://doi.org/10.26713/cma.v12i3.1597

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Section

Research Article