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.

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.

background: in vivo dosimetry is a method for estimation of overall error in the delivered dose to the patients at the end of radiotherapy process. in this research, two methods for target dose calculation were evaluated on midline and central axis of photon beams in in vivo dosimetry of thorax fields. materials and methods: entrance and exit doses for anterior and lateral fields of thorax were...