The general Randić index Rα(G) of a (chemical) graph G, is defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α an arbitrary real number, which is called the Randić index or connectivity index (or branching index) for α = −1/2 proposed by Milan Randić in 1975. The paper outlines the results known for the (general) Randić inde...

Quantitative structure-toxicity relationship (QSTR) plays an important role in toxicity prediction. With the modified method, the quantum chemistry parameters of 57 benzoic acid compounds were calculated with modified molecular connectivity index (MCI) using Visual Basic Program Software, and the QSTR of benzoic acid compounds in mice via oral LD(50) (acute toxicity) was studied. A model was bu...

Given a connected graph G, the Randić index R(G) is the sum of 1 √ d(u)d(v) over all edges {u, v} of G, where d(u) and d(v) are the degree of vertices u and v respectively. Let q(G) be the largest eigenvalue of the singless Laplacian matrix of G and n = |V (G)|. Hansen and Lucas (2010) made the following conjecture:

In this paper, we defined a novel delta value di in molecular connectivity, and then obtained a novel kind of valence molecular connectivity index. The potential usefulness of the novel kind of valence molecular connectivity index in QSAR/QSPR is evaluated by its correlation with a number of molecules and by a favorable comparison with models based on molecular connectivity index. q 2003 Elsevi...

‎the second multiplicative zagreb coindex of a simple graph $g$ is‎ ‎defined as‎: ‎$${overline{pi{}}}_2left(gright)=prod_{uvnotin{}e(g)}d_gleft(uright)d_gleft(vright),$$‎ ‎where $d_gleft(uright)$ denotes the degree of the vertex $u$ of‎ ‎$g$‎. ‎in this paper‎, ‎we compare $overline{{pi}}_2$-index with‎ ‎some well-known graph invariants such as the wiener index‎, ‎schultz‎ ‎index‎, ‎eccentric co...

Randić index, R, also known as the connectivity or branching index, is an important topological index in chemistry. In order to attack some conjectures concerning Randić index, Dvořák et al. [5] introduced a modification of this index, denoted by R′. In this paper we present some of the basic properties of R′. We determine graphs with minimal and maximal values of R′, as well as graphs with min...

In this note, we derive the lower bound on the sum for Wiener index of bipartite graph and its bipartite complement, as well as the lower and upper bounds on this sum for the Randić index and Zagreb indices. We also discuss the quality of these bounds.

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