Chemical compounds and drugs are often modelled as graphs (for example, Polyhex Nanotubes and Dendrimer Nanostar) 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. The edge Wiener index of ...

Graphs are used to model chemical compounds and drugs. In the graphs, each vertex represents an atom of molecule and edges between the corresponding vertices are used to represent covalent bounds between atoms. We call such a graph, which is derived from a chemical compound, a molecular graph. Evidence shows that the vertex-weighted Wiener number, which is defined over this molecular graph, is ...

In this paper we present a bond graph model of a Continuous Stirred Tank Reactor which represents the reaction kinetics as well as the heat and mass transport phenomena in the reactor. The consequences of reticulation of the phenomena and of the systematic use of the power conjugated variables on the formulation of the thermodynamic properties, the reaction kinetics and the energy and mass tran...

Simple random walks probabilistically grown step by step on a graph are distinguished from walk enumerations and associated equipoise random walks. Substructure characteristics and graph invariants correspondingly defined for the two types of random walks are then also distinct, though there often are analogous relations. It is noted that the connectivity index as well as some resistance-distan...

it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

Supervised learning on graphs is a central subject in graph data processing. In graph classification and regression, we assume that the target values of a certain number of graphs or a certain part of a graph are available as a training dataset, and our goal is to derive the target values of other graphs or the remaining part of the graph. In drug discovery applications, for example, a graph an...

This report briefly describes the development and applications of net-sign graph theory. The current work enunciates the graph (molecule) signature of nonalternant non-benzenoid hydrocarbons with odd member of rings (non-bipartite molecular graphs) based on chemical signed graph theory. Experimental evidences and Hückel spectrum reveal that structure possessing nonbonding molecular orbital (NBM...