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.

In this paper, we introduce and study a new distance parameter {\it triameter} of connected graph $G$, which is defined as $max\{d(u,v)+d(v,w)+d(u,w): u,v,w \in V\}$ denoted by $tr(G)$. We find various upper lower bounds on $tr(G)$ in terms order, girth, domination parameters etc., characterize the graphs attaining those bounds. process, provide some (connected, total) numbers its triameter. Th...

In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and on the product of the chromatic number of a graph and its complement, in terms of the order of the graph. Since then, relations of a similar type have been proposed for many other graph invariants, in several hundred papers. We present a survey on this research endeavor.