Some Results on Strong Edge Geodetic Problem in Graphs - Xavier, D. Antony; Mathew, Deepa; Theresal, Santiagu; Varghese, Eddith Sarah (Communications in Mathematics and Applications, 2020)
For a graph \(G(V(G),E(G))\), the problem to find a \(SV(G)\) where every edge of the graph \(G\) is covered by a unique fixed geodesic between the pair of vertices in \(S\) is called the strong edge geodetic problem and the cardinality of the smallest such \(S\) is the strong edge geodetic number of \(G\). In this paper the strong edge geodetic problem for product graphs are studied and also some results for general graphs are derived.