The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Turán graphs frequently appear in extremal graph theory. We show that Turán graphs and a conne...

The sum of distances between all pairs of vertices W (G) in a connected graph G as a graph invariant was first introduced by Wiener [9] in 1947. He observed a correlation between boiling points of paraffins and this invariant, which has later become known as Wiener index of a graph. Today, the Wiener index is one of the most widely used descriptors in chemical graph theory. Due to its strong co...

the fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. in this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. so ,  a novel method for computing the new descriptors to construct a quantitative rela...

We develop a binary relaxation scheme for graph matching in chemical databases. The technique works by iteratively pruning the list of matching possibilities for individual atoms based upon contextual information. Its key features include delayed decision-making, robustness to noise, and fast and eecient neural implementation. We illustrate the utility of the technique by comparing it with prob...

the do1(18c6)fi (mwli. na. k and i 8c6=18-crown-6) complexes have been chosen as the model systems toinvestigate the nature of chemical bonds between alkali metal cations and large mffitidentaie orgmnic ligands.the b3lyp/6-3i+g(d,p) level of calculation has been used for obtaining equilibrium geernetnes and p(r)functions (electron density distributions). by the aid of fundamental physical theor...

Let G be a simple connected graph in chemical graph theory and uν e = be an edge of G. The Randić index ( ) G χ and sum-connectivity ( ) G X of a nontrivial connected graph G are defined as the sum of the weights ν ud d 1 and ν u d d + 1 over all edges ν u e = of G, respectively. In this paper, we compute Randić ( ) G χ and sum-connectivity ( ) G X indices of V-phenylenic nanotubes and nanotori.

The focus of this chapter will be the uses of graph theory in chemoinformatics and in structural bioinformatics. There is a long history of chemical graph theory dating back to the 1860’s and Kekule’s structural theory. It is natural to regard the atoms of a molecule as nodes and the bonds as edges (2D representations) of a labeled graph (a molecular graph). This chapter will concentrate on the...

In [13] co graphs are introduced and a formula is given for the PI index of these graphs. Based on this formula a new topological CI index is proposed. In this note it is observed that co graphs are precisely isometric subgraphs of hypercubes alias partial cubes. Some fact about partial cubes and their uses in chemical graph theory are listed. A couple of comments on the CI index are also given...