Double Geodetic Number of a Line Graph

Abstract

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.