Let G be a graph. In this paper, we study the eccentric connectivity index, the new version of the second Zagreb index and the forth geometric–arithmetic index.. The basic properties of these novel graph descriptors and some inequalities for them are established.

the concept of geometric-arithmetic indices was introduced in the chemical graph theory.these indices are defined by the following general formula:   ( )2( ) uv e g u vu vq qq qga g ,where qu is some quantity that in a unique manner can be associated with the vertex u ofgraph g. in this paper the exact formula for two types of geometric-arithmetic index of vphenylenicnanotube are given.

Dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core [1,4]. These are key molecules in nanotechnology and can be put to good use. In this article, we compute the first geometricarithmetic index of two infinite classes of dendrimers.

The total version of geometric–arithmetic index of graphs is introduced based on the endvertex degrees of edges of their total graphs. In this paper, beside of computing the total GA index for some graphs, its some properties especially lower and upper bounds are obtained.

particulate matters commonly found dispersed in the atmosphere are composed of a large variety of substances. dustfall is the usual index of particles in the size range greater than 10 m. two semi automated so2 sampling units were installed in tehran university campus (from 21 january 1973 to 22 dec. 1974) and gheitarieh area (from 23 august to 23 oct. 1974) hydrogen peroxide method was used fo...

Recently, the arithmetic–geometric index (AG) was introduced, inspired by well-known and studied geometric–arithmetic (GA). In this work, we obtain new bounds on index, improving upon some already known bounds. particular, show families of graphs where such are attained.

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.

In this paper we describe a C++ implementation of a hybrid system combining SLI (symmetric level-index) arithmetic and FLP (floating-point) arithmetic. The principal motivation for the work to be presented is to promote the use of SLI arithmetic as a practical framework for scientific computing. This hybrid arithmetic is essentially overflow and underflow free, and its implementation has shown ...

the geometric-arithmetic index is another topological index was defined as2 deg ( )deg ( )( )deg ( ) deg ( )g guv eg gu vga gu v  , in which degree of vertex u denoted by degg (u). wenow define a new version of ga index as 4( )2 ε ( )ε ( )( )ε ( ) ε ( )g ge uv e g g gu vga g  u v , where εg(u) isthe eccentricity of vertex u. in this paper we compute this new topological index for twogr...