The concept of geometric−arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric−arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus−Gaddum−type results for GA2.

Background: The seeds of some medicinal plants and their compounds have long been valued for their numerous health benefits. Objective:To investigate some physical and chemical properties of Salvia spp. Methods: Some physico-chemical properties in five species of Salvia seeds (consisted of S. officinalis L., S. macrosiphon L., S. hypoleuca L., S. sclarea L. and S. nemorosa L.) were measured ...

The geometric-arithmetic index is another topological index was defined as 2 deg ( )deg ( ) ( ) deg ( ) deg ( ) G G uv E G G u v GA G u v     , in which degree of vertex u denoted by degG (u). We now define a new version of GA index as 4 ( ) 2 ε ( )ε ( ) ( ) ε ( ) ε ( ) G G e uv E G G G u v GA G   u v    , where εG(u) is the eccentricity of vertex u. In this paper we compute this new t...

background: the seeds of some medicinal plants and their compounds have long been valued for their numerous health benefits. objective:to investigate some physical and chemical properties of salvia spp. methods: some physico-chemical properties in five species of salvia seeds (consisted of s. officinalis l., s. macrosiphon l., s. hypoleuca l., s. sclarea l. and s. nemorosa l.) were measured at ...

The geometric-arithmetic index of graph G is defined as GA(G) = ∑ uv∈E(G) 2 √ dudv du+dv , du (or dv) is the degree the vertex u (or v). The GA index of benzenoid systems and phenylenes are computed, a simple relation is established between the geometric-arithmetic of a phenylene and the corresponding hexagonal squeeze in this paper. Mathematics Subject Classification: 05C05, 05C12

A topological descriptor is regarded as a numerical parameter derived by using mathematical tools from the molecular graph of different chemical structures. The theory paramount section chemistry. In this section, there are many parameters, that have very useful characteristics to study structure chemicals. article, we investigate indices concealed non-kekulean benzenoid hydrocarbon graph. We w...

Let G = (V,E), V {1,2,...,n}, be a simple connected graph of order n, size m with vertex degree sequence d1 ? d2 ... dn > 0, di d(vi). The geometric-arithmetic topological index is defined as GA(G) i~j 2? didj/di+dj, whereas the coindex GA?(G) i~/j 2 didj/di+dj . New lower bounds for and in terms some parameters other invariants are obtained.

Many classical inequalities are just statements about the convexity or concavity of certain (hidden) underlying functions. This is nicely illustrated by Hardy, Littlewood, and Pólya [5] whose Chapter III deals with “Mean values with an arbitrary function and the theory of convex functions,” and by Steele [12] whose Chapter 6 is called “Convexity—The third pillar.” Yet another illustration is th...