The aim of this paper is to briefly present the Bond Graph language and the advantages that one can get from its use. The main point is the easy reusability of the sub-models that are the basis of a given model. The Bond Graph language has been firstly developed for the modeling of finite dimension systems in mechatronic and electrical engineering but it can also be applied to infinite dimensio...

‎in this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $c_4$-free.‎

In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of chemical kinetics, such as mass-action kinetics, Michaelis-Menten kinetics, etc. Our results relate previously described linear algebraic and graph-theoretic con...

Integrating data involving chemical structures is simplified when unique identifiers (UIDs) can be associated with chemical structures. For example, these identifiers can be used as database keys. One common approach is to use the Unique SMILES notation introduced in [2]. The Unique SMILES views a chemical structure as a graph with atoms as nodes and bonds as edges and uses a depth first traver...

Evolution produces complex and structured networks of interacting components in chemical, biological, and social systems. We describe a simple mathematical model for the evolution of an idealized chemical system to study how a network of cooperative molecular species arises and evolves to become more complex and structured. The network is modeled by a directed weighted graph whose positive and ...

This paper compares several published methods for clustering chemical structures, using both graph- and fingerprint-based similarity measures. The clusterings from each method were compared to determine the degree of cluster overlap. Each method was also evaluated on how well it grouped structures into clusters possessing a non-trivial substructural commonality. The methods which employ adjusta...

The search of molecular structures inside a large database of chemical compounds is a critical step for many computer programs used in several domains of chemistry. During the last years, the size of many chemical databases has dramatically increased, hence in the meantime, search engines needed to be more and more powerful. The speed and the efficiency of screening processes of the chemical co...

Mapping the chemical space of small organic molecules is approached from a theoretical graph theory viewpoint, in an effort to begin the systematic exploration of molecular topologies. We present an algorithm for exhaustive generation of scaffold topologies with up to eight rings and an efficient comparison method for graphs within this class. This method uses the return index, a topological in...

The interpretation of topological resonance energy (TRE), the mathematical measure of energetic chemical aromaticity at the Hückel level of theory, is revisited by providing a concise analysis of the matching polynomial of a chemical graph. Whereas the matching (or acyclic) polynomial is not a properly characteristic polynomial in general, it is the arithmetic mean of the characteristic polynom...

In drug discovery, one key step is to predict chemical activities of drug candidates such as toxicity, mutagenicity and solubility and thereby reduce the number of chemical compounds screened by actual experimental means. Such computational prediction is called “virtual screening”. Drug candidates are small molecules which are represented as attributed graphs where atoms and bonds correspond to...