We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two submanifolds. The key role of the theory is played by the notion of the Maslov index of a semi-Riemannian geodesic, which is a homological invariant and it substitutes the notion of geometric index in Riemannian geome...

The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper–Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

We give sharp upper bounds on the Zagreb indices and lower bounds on the Zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.

1. Abstract theory. Let M be a C-Riemannian manifold without boundary modeled on a separable Hubert space (see Lang [3]). For pÇzM we denote by ( , )p the inner product in the tangent space Mp and we define a function || || on the tangent bundle T(M) by ||z>|| = (v, v)J for vÇzMp. Given p and q in the same component of M we define p(p, q)==lnïfl\\<r'(t)\\dtt where the Inf is over all C 1 paths ...