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The atom-bond connectivity index (ABC) is a degree-based molecular structure descriptor with well-documented chemical applications. In 2010 a distance-based new variant of this index (ABCGG) has been proposed. Until now, the relation between ABC and ABCGG has not been analyzed. In this paper, we establish the basic characteristics of this relation. In particular, ABC and ABCGG are not correlated and both cases ABC > ABCGG and ABC < ABCGG may occur in the case of (structurally similar) molecules. However, in the case of benzenoid hydrocarbons, ABC always exceeds ABCGG. [Projekat Ministarstva nauke Republike Srbije, br. 174033]

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The Graovac–Ghorbani index ( ABC GG ), was introduced by Graovac and Ghorbani, (2010). In this paper we present some upper and lower bounds on the ABC GG index and characterize the extremal graphs. [ABSTRACT FROM AUTHOR]

The zeroth-order Randić index and the sum-connectivity index are very popular topological indices in mathematical chemistry. These two indices are based on vertex degrees of graphs and attracted a lot of attention in recent years. Recently Li and Li (2015) studied these two indices for trees of order n . In this paper we obtain a relation between the zeroth-order Randić index and the sum-connectivity index for graphs. From this we infer an upper bound for the sum-connectivity index of graphs. Moreover, we prove that the zeroth-order Randić index is greater than the sum-connectivity index for trees. Finally, we show that R 2,  α ( G ) is greater or equal R 1,  α ( G ) ( α ≥ 1) for any graph and characterize the extremal graphs. [ABSTRACT FROM AUTHOR]

Abstract: For a (molecular) graph, the first Zagreb index is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index is equal to the sum of the products of the degrees of pairs of adjacent vertices. If is a connected graph with vertex set , then the eccentric connectivity index of , , is defined as, , where is the degree of a vertex and is its eccentricity. In this report we compare the eccentric connectivity index () and the Zagreb indices ( and ) for chemical trees. Moreover, we compare the eccentric connectivity index () and the first Zagreb index () for molecular graphs. [Copyright &y& Elsevier]

Abstract: The recently introduced atom-bond connectivity () index has been applied up until now to study the stability of alkanes and the strain energy of cycloalkanes. Furtula et al. (2009) obtained extremal values for chemical trees, and also, it has been shown that the star , has the maximal value of trees. In this paper, we present the lower and upper bounds on index of graphs and trees, and characterize graphs for which these bounds are best possible. [Copyright &y& Elsevier]

Abstract: Lower and upper bounds on Szeged index of connected (molecular) graphs are established as well as Nordhaus–Gaddum-type results, relating the Szeged index of a graph and of its complement. [Copyright &y& Elsevier]