Strong Upper Geodetic Number of Graphs - Infanta, L. G. Bino; Xavier, D. Antony (Communications in Mathematics and Applications, 2021)
Let \(G=(V,E)\) be a graph. A set \(SG\) is a strong geodetic set, if each vertex \(vG/S\) 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.