On the Geodetic Cover and Geodetic Basis of the Corona of Graphs

Abstract

Any path of length distG (u, v) is a u-v geodesic in G, where u and v are vertices of a connected graph G. The set I [u, v] denotes the closed interval consisting of u, v and. all vertices lying on some u-v geodesic. If A C V (G), then I[A] is the union of all sets I[u, v] for all u, v ∈ A. If I[ A) = V ( G), then A is a geodetic cover. A geodetic cover of minimum cardinality is called a geodetic basis.

The corona of graphs G and H is the graph obtained by taking a copy of G of order n and n copies of H, and then joining the ith vertex of G to every vertex in the ith copy of H. In this paper, we give the order of the geodesic basis of the corona of two connected graphs.