The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...

This paper considers the truncation of matroids and geometric lattices. It is shown that the truncated matroid of a representable matroid is again representable. Truncation formulas are given for the coboundary and Möbius polynomial of a geometric lattice and the spectrum polynomial of a matroid, generalizing the truncation formula of the rank generating polynomial of a matroid by Britz. Mathem...

The aim of this paper is to set a foundation to separate geometric model theory from model theory. Our goal is to explore the possibility to extend results from geometric model theory to non first order logic (e.g. L! 1;! ). We introduce a dependence relation between subsets of a pregeometry and show that it satisfies all the formal properties that forking satisfies in simple first order theori...