Strong Upper Geodetic Number of Graphs
DOI:
https://doi.org/10.26713/cma.v12i3.1597Keywords:
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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