Graph orbits and complexity of topological index

Let I be a summation-type topological index and let G be a graph. The I-complexity CI (G) of G is introduced as the number of di erent contributions to I(G) in its summation formula. The complexity is studied in the case of the connective eccentric index ce and Szeged index. It is proved that C ce (G) Ov(G) and CS z(G) Oe(G) where Ov(G) and Oe(G) are the number of di erent vertex orbits and edge orbits of G respectively. Graphs with C ce (G) = 1 and CS z(G) = 1 are studied.