Wiener complexity and eccentric complexity of graphs

Let G be a simple connected graph. Transmission of vertex v is defined as sum of distances between v and the other vertices. Wiener complexity (resp. eccentric complexity) of graph G, CW(G), (resp. Cec(G)) is introduced as number of different transmissions (resp. eccentricities) among all vertices of G. in this paper, some structural properties of graph G which CW(G) = |V (G)| is investigated. It is proved that such graphs have diameter at least 3. For any integer m, an infinite family of graphs is constructed that the CW(G) = Cec(G) = m.