Double Geodetic Number of a Line Graph
Ayarlin Kirupa M., T. Jebaraj · Mapana Journal of Sciences · 2023
Any line graph L(G), whose vertices correspond to the edges of G(V, E) and two vertices in L(G) are adjacent if and only if the corresponding edges in G are adjacent. If there are vertices u, v in S such that x, y ∈ I[u, v] for any pair of vertices x, y in G, then the set S of vertices of G is said to be a double geodetic set of G. The lowest cardinality of a double geodetic set is represented by the double geodetic number dg(G). In this study, we determine double geodetic number of several line graphs’ double geodetic numbers.