An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...

Several different topological indices (the carbon number, the Wiener index, the Balaban dis­ tance sum connectivity index, the Randic molecular identification number, and the Randic molecular connectivity indices °/, 2%, 3̂ p and 3/ c) were employed in the correlation of the velocity of ultrasonic sound in a variety of alkane and alcohol species. Using linear regression analyses and published so...

In this paper, we present some new lower and upper bounds for the modified Randic index in terms of maximum, minimum degree, girth, algebraic connectivity, diameter and average distance. Also we obtained relations between this index with Harmonic and Atom-bond connectivity indices. Finally, as an application we computed this index for some classes of nano-structures and linear chains.

Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indic...

We prove that, for any graph G, its energy is at least twice the Randic index. show that equality holds if and only G union of complete bipartite graphs.

We introduce a partial order on the collection of chemical trees based on tree transformations. This partial order is tightly related to the Randić connectivity index χ. Its analysis provides new structural information about the behavior of χ. As an illustration of the approach presented, we give a different and more structural view of some known results about the first values of χ on the colle...

We discuss some features of the orthogonalization methods commonly applied to QSPR QSAR studies. We outline the well known multivariable linear regression analysis in vector form in order to compare mainly Randic and Gram-Schmidt orthogonalization procedures and also cast the basis for other approaches like Löwdin’s one. We expect that present review may become the starting point for future dev...

How much of the combinatorial structure of a pointed polyhedron is contained in its vertex-facet incidences? Not too much, in general, as we demonstrate by examples. However, one can tell from the incidence data whether the polyhedron is bounded. In the case of a polyhedron that is simple and “simplicial,” i.e., a d-dimensional polyhedron that has d facets through each vertex and d vertices on ...