the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery 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-typeresults for ga2.

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

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 first geometric-arithmetic index was introduced in the chemical theory as the summationof 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertexu. in this paper we give the expressions for computing the first geometric-arithmetic index ofhexagonal systems and phenylenes and present new method for describing hexagonal systemby corresponding a simple graph...

‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...

Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric-arithmetic index of graphs, Iran. J. Math Chem., 1(2) (2010) 17-28, 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.

Partition of unity parametrics (PUPs) are a recent framework designed for geometric modeling. We propose employing PUPs for procedural texture synthesis, taking advantage of the framework’s guarantees of high continuity and local support. Using PUPs to interpolate among data values distributed through the plane, the problem of texture synthesis can be approached from the perspective of point pl...

‎In this paper first we define the morphism between geometric spaces in two different types‎. ‎We construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎The relation between hypergroups and geometric spaces is studied‎. ‎By constructing the category $qh$ of $H_{v}$-groups we answer the question...