For a connected graph G, the eccentric connectivity index (ECI) and the first Zagreb eccentricity index of G are defined as ( ) ( ) deg ( ) ( ) i c G i G i v V G ξ G v ε v   and ( 2 1 ) ( ) ( ) i G i v G V E G ε v   , respectively, where deg ( ) G i v is the degree of i v in G and ( ) G i ε v denotes the eccentricity of vertex i v in G. In this paper we compare the eccentric connectivity ...

The concept of Zagreb eccentricity indices ( 1 E and 2 E ) was introduced in the chemical graph theory very recently. The eccentric connectivity index ( ) c ξ is a distance-based molecular structure descriptor that was used for mathematical modeling of biological activities of diverse nature. The second geometric-arithmetic index 2 ( ) GA was introduced in 2010, is found to be useful tool in QS...

For a nontrivial graph G, its first Zagreb coindex is defined as the sum of degree sum over all non-adjacent vertex pairs in G and the second Zagreb coindex is defined as the sum of degree product over all non-adjacent vertex pairs in G. Till now, established results concerning Zagreb coindices are mainly related to composite graphs and extremal values of some special graphs. The existing liter...

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.

tures, that is, chemical compounds, intermediates, changes and mechanisms. Over the past decades graph-based molecular structure descriptors have developed into a quite active field. In these applications a molecular structure is identified to a graph, with vertices representing non-H atoms and edges representing chemical bonds. During the last decade the interest in the problem of computer-aid...