Strong Open Monophonic Number of a Graph - Varghese, Eddith Sarah; Xavier, D. Antony; Mathew, Deepa; Raja, S. Arul Amirtha (Communications in Mathematics and Applications, 2021)
For a graph \(G(V,E)\), the strong open monophonic problem is to find a set \(S\subseteq V (G)\) such that each vertex in \(V(G)\) lies on a unique fixed monophonic path between the vertices in \(S\) and the set \(S\) is called the strong open monophonic set. In this paper, we have discussed some results related to strong open monophonic sets and mainly we have the complexity property of strong open monophonic set problem for general graph. Also, some bounds for general graphs are derived.
Keywords: Strong geodetic number; Monophonic set; Monophonic number; Strong open monophonic number