Let G be a simple connected graph and di be the degree of its ith vertex. In a recent paper [D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 1369–1376] the ‘‘first geometric–arithmetic index’’ of a graph Gwas defined as GA1 = − di dj (di + dj)/2 with summation going over all pairs of ...

The second geometric-arithmetic index GA2(G) of a graph G was introduced recently by Fath-Tabar et al. [2] and is defined to be ∑ uv∈E(G) √ nu(e,G)nv(e,G) 1 2 [nu(e,G)+nv(e,G)] , where e = uv is one edge in G, and nu(e,G) denotes the number of vertices in G lying closer to u than to v. In this paper, we characterize the tree with the minimum GA2 index among the set of trees with given order and...

The edge and total versions of geometric-arithmetic (GA) index of graphs are introduced based on the end-vertex degrees of edges of their line and total graphs, respectively. In this paper, the edge and total GA indices are computed for some graphs by using some results on GA index and graphs.

The total version of geometric–arithmetic (GA) index of graphs is introduced based on the end-vertex degrees of edges of their total graphs. In this paper, the total GA index is computed for zigzag polyhex nanotubes by using some results on GA index and mentioned nanotubes. Also, we compute the edge GA index for the subdivision graphs of TUC C (R) and TUAC [p',q'] nanotubes. 4 8 6

9] for example, and, in this paper, we introduce an index In this paper we present a rigorous theoretical analysis of the main properties of a double base number system, using bases 2 and 3; in particular we emphasize the sparseness of the representation. A simple geometric interpretation allows an efficient implementation of the basic arithmetic operations and we introduce an index calculus fo...