The geodesic-transversal problem on complementary prisms

A maximal geodesic in a graph is a geodesic which is not a sub-path of a longer geodesic. A subset S of vertices of a graph G is called a geodesic transversal of G if every maximal geodesic of G intersects S. The geodesic transversal problem aims to find the minimum cardinality of such a set and its cardinality is denoted by gt(G). In this work, we determine gt(G) for complementary cycle graphs, complementary path graphs, complete multipartite graph, complete split graphs, wheel graphs, fan graphs and butterfly graphs, and their complementary prisms. We also find an upper bound of gt(G) of butterfly network.