The concept of geometric-arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.

Chemical compounds and drugs are often modelled as graphs where each vertex represents an atom of molecule, and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph, and can be different structures. In this paper, by virtue of mathematical derivation, we determine the fourth, f...

In this paper we introduce a novel graph classification algorithm and demonstrate its efficacy in drug design. In our method, we use graphs to model chemical structures and apply a wavelet analysis of graphs to create features capturing graph local topology. We design a novel graph kernel function to utilize the created feature to build predictive models for chemicals. We call the new graph ker...

Chemical compounds and drugs are often modeled as graphs where each vertex represents an atom of molecule, and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph, and can be different structures. In this paper, we determine the logarithm multiplicative Wiener index and recipr...

Abstract. 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. A graph is a ...

abstract. 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 us...

Graph reduction is an implementation technique for the lazy λ-calculus. It has been used to implement many non-strict functional languages, such as lazy ML, Gofer and Miranda. Parallel graph reduction allows for concurrent evaluation. In this paper, we present parallel graph reduction as a Chemical Abstract Machine, and show that the resulting testing semantics is adequate wrt testing equivalen...

Graph rewrite systems are powerful tools to model and study complex problems in various fields of research. Their successful application to chemical reaction modelling on a molecular level was shown but no appropriate and simple system is available at the moment. The presented Graph Grammar Library (GGL) implements a generic Double Push Out approach for general graph rewrite systems. The framew...

Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their ch...