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

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.

Let G be a simple connected graph and di be the degree of its ith vertex. In a recent paper [D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 1369–1376] the ‘‘first geometric–arithmetic index’’ of a graph Gwas defined as GA1 = − di dj (di + dj)/2 with summation going over all pairs of ...

The second geometric-arithmetic index GA2(G) of a graph G was introduced recently by Fath-Tabar et al. [2] and is defined to be ∑ uv∈E(G) √ nu(e,G)nv(e,G) 1 2 [nu(e,G)+nv(e,G)] , where e = uv is one edge in G, and nu(e,G) denotes the number of vertices in G lying closer to u than to v. In this paper, we characterize the tree with the minimum GA2 index among the set of trees with given order and...