Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric−arithmetic index of graphs, Iran. J. Math Chem., 1 (2010) 17−27, in this paper we present lower and upper bounds on the third geometric−arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus−Gaddum−type result for GA3.

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...

In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.

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 index is a function having set of graphs as its domain and real numbers range. Here we concentrated on indices involving the number vertices, edges maximum minimum vertex degree. The aim this paper to compute lower upper bounds second Zagreb index, third Hyper Harmonic Redefined first First reformulated Forgotten square F-index, Sum-connectivity Randic Reciprocal Gourava Sombar Ni...

Here, we initiate a program to study relationships between finite groups and arithmetic–geometric invariants in systematic way. To do this, first introduce notion of optimal module for group the setting holomorphic mock Jacobi forms. Then, classify modules cyclic prime order, special case weight 2 index 1, where class numbers imaginary quadratic fields play an important role. Finally, exhibit c...