the atom bond connectivity index of a graph is a new topological index was defined by e.estrada as abc(g)  uve (dg(u) dg(v) 2) / dg(u)dg(v) , where g d ( u ) denotes degreeof vertex u. in this paper we present some bounds of this new topological index.

wiener index is a topological index based on distance between every pair of vertices in agraph g. it was introduced in 1947 by one of the pioneer of this area e.g, harold wiener. inthe present paper, by using a new method introduced by klavžar we compute the wiener andszeged indices of some nanostar dendrimers.

The atom-bond connectivity (ABC) index is a degree-based molecular descriptor, that found chemical applications. It is well known that among all connected graphs, the graphs with minimal ABC index are trees. A complete characterization of trees with minimal ABC index is still an open problem. In this paper, we present new structural properties of trees with minimal ABC index. Our main results r...

The atom-bond connectivity (ABC) index is a degree-based graph topological index that found chemical applications. The problem of complete characterization of trees with minimal ABC index is still an open problem. In [14], it was shown that trees with minimal ABC index do not contain so-called Bk-branches, with k ≥ 5, and that they do not have more than four B4-branches. Our main results here r...

The atom-bond connectivity index—abbreviated ABC—has proven to describe the heat of formation of alkanes with an accuracy comparable to that of high-level ab initio and DFTmethods. Its physical interpretation in terms of quantumtheory, its generalization, and many of its mathematical properties have been reported. Here, a probabilistic interpretation of the generalized ABC index is provided. It...

In this talk we consider some results and open problems from the Chemical Graph Theory, mainly concerning structural indices/properties. The Atom Bond Connectivity index, also known as ABC index was defined by Estrada [4] with relation to the energy of formation of alkanes. It was quickly recognized that this index reflects important structural properties of graphs in general. The ABC index was...

The atom-bond connectivity (ABC) index is a recently introduced topological index, defined as ABC(G) = ∑ uv∈E(G) √ du+dv−2 dudv , where du (or dv) is the degree the vertex u (or v). The ABC index of benzenoid systems and phenylenes are computed, a simple relation is established between the atom-bond connectivity index of a phenylene and the corresponding hexagonal squeeze in this paper. Mathema...

The atom-bond connectivity (ABC) index is one of the recently most investigated degree-based molecular structure descriptors, that have applications in chemistry. For a graph G, the ABC index is defined as ∑ uv∈E(G) √ (d(u)+d(v)−2) d(u)d(v) , where d(u) is the degree of vertex u in G and E(G) is the set of edges of G. Despite many attempts in the last few years, it is still an open problem to c...

Introduction External validation of four nephrometry scores (NS): Centrality index (C-index), arterial based complexity (ABC), preoperative aspects and dimensions used for an anatomical (PADUA) and radius expohytic/endophytic nearness anterior/posterior location (RENAL) scoring systems in patients who have undergone trans-peritoneal robotic assisted partial nephrectomy (RAPN). Material and me...