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...

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.

introduction echo-planar imaging (epi) is a group of fast data acquisition methods commonly used in fmri studies. it acquires multiple image lines in k-space after a single excitation, which leads to a very short scan time. a well-known problem with epi is that it is more sensitive to distortions due to the used encoding scheme. source of distortion is inhomogeneity in the static b0 field that ...