The atom-bond connectivity (ABC) index of a graph ( , ) G V E is defined as ( ) [ ( ) ( ) 2] / [ ( ) ( )] uv E ABC G d u d v d u d v , where ( ) d u denotes the degree of vertex u of G . This recently introduced molecular structure descriptor found interesting applications in the study of the thermodynamic stability of acyclic saturated hydrocarbons, and the strain energy of their cyclic congen...

The atom-bond connectivity (ABC) index is a degree-based molecular structure descriptor that can be used for modelling thermodynamic properties of organic chemical compounds. Motivated by its applicable potential, a series of investigations have been carried out in the past several years. In this note we first consider graphs with given edge-connectivity that attain the maximum ABC index. In pa...

The atom-bond connectivity (ABC) index is one of the most investigated degreebased molecular structure descriptors with a variety of chemical applications. It is known that among all connected graphs, the trees minimize the ABC index. However, a full characterization of trees with a minimal ABC index is still an open problem. By now, one of the proved properties is that a tree with a minimal AB...

The atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are two well-studied topological indices, which are useful tools in QSPR and QSAR investigations. In this paper, we first obtain explicit formulae for the expected values of ABC and GA indices in random spiro chains, which are graphs of a class of unbranched polycyclic aromatic hydrocarbons. Based on these formulae, we t...

The atom-bond connectivity (ABC) index, introduced by Estrada et al. in 1998, displays an excellent correlation with the formation heat of alkanes. We give upper bounds for this graph invariant using the number of vertices, the number of edges, the Randić connectivity indices, and the first Zagreb index. We determine the unique tree with the maximum ABC index among trees with given numbers of v...

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 degree of vertex u. In this paper we present some bounds of this new topological index.

In this paper, we compute ABC index, Randic connectivity index, Sum connectivity index, GA index, Harmonic index, General Randic index of Triglyceride. AMS subject classification:

The atom-bond connectivity (ABC) index of a graph ( , ) G V E is defined as ( ) [ ( ) ( ) 2] / [ ( ) ( )] i j i j i j v v E ABC G d v d v d v d v , where ( ) i d v denotes the degree of the vertex i v of G . This recently introduced molecular structure descriptor found interesting applications in the study of the heats of formation of alkanes. Let ( ) C and ( ) T denote the sets of connected gr...

Suppose A, B, C, D, E, F are points and L is a line other than the line at infinity. This work examines cases in which a translation D′E′F ′ of DEF in the direction of L is perspective to ABC, in the sense that the lines AD′, BE′, CF ′ concur.

Surface modification of nanocarriers with amphiphilic polymer polyethylene glycol (PEG), known as PEGylation, is regarded as a major breakthrough in the application of nanocarriers. However, PEGylated nanocarriers (including liposomes and polymeric nanoparticles) induce what is referred to as the "accelerated blood clearance (ABC) phenomenon" upon repeated injection and consequently they lose t...