The concept of atom-bond connectivity (ABC) index was introduced in the chemical graph theory in 1998. The atom-bond connectivity (ABC) index of a graph G defined as (see formula in text) where E(G) is the edge set and di is the degree of vertex v(i) of G. Very recently Graovac et al. define a new version of the ABC index as (see formula in text) where n(i) denotes the number of vertices of G w...

Among topological descriptors, connectivity indices are very important and they have a prominent role in chemistry. One of them is atom-bond connectivity (ABC) index of a connected graph G=(V,E) and defined as where d denotes the degree of vertex v of G, that introduced by Furtula v and et.al. Also, in 1997, Sharma, Goswami and Madan introduced the eccentric connectivity index of the molecular ...

A topological index is a function which associates real number to the graphs. Graph theory is significant in the subject of structural chemistry. In this paper we calculated Rα, Mα, χα, ABC, GA, ABC4 and GA5 indices of L(S(CNCk[n])). AMS (MOS) Subject Classification Codes: 05C07

For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to the vertex u than to the vertex v and nv= n(v|G) can be defined simailarly. Then the ABCGG index of G is defined as ABC...

the atom-bond connectivity index of graph is a topological index proposed by estrada et al.as abc (g)  uve (g ) (du dv  2) / dudv , where the summation goes over all edges ofg, du and dv are the degrees of the terminal vertices u and v of edge uv. in the present paper,some upper bounds for the second type of atom-bond connectivity index are computed.

The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for  ABCa index for cacti of order $n$ ...

The atom-bond connectivity index of graph is a topological index proposed by Estrada et al. as ABC (G)  uvE (G ) (du dv  2) / dudv , where the summation goes over all edges of G, du and dv are the degrees of the terminal vertices u and v of edge uv. In the present paper, some upper bounds for the second type of atom-bond connectivity index are computed.

Among topological descriptors connectivity topological indices are very important and they have a prominent role in chemistry. One of them is atom-bond connectivity (ABC) index defined as ABC(G)= [formula:see text], in which degree of vertex v denoted by dv . Recently, a new version of atom-bond connectivity (ABC4) index was introduced by M. Ghorbani et.al in 2010 and is defined as ABC4(G)= [fo...

The atom-bond connectivity (ABC) index is a degree-based molecular descriptor that found diverse chemical applications. Characterizing trees with minimum ABC-index remained an elusive open problem even after serious attempts and considered by some as one of the most intriguing problems in mathematical chemistry. In this paper, we describe exact structure extremal sufficiently many vertices show...