The pioneering contributions of cayley and sylvester to the mathematical description of chemical structure

Some New Trends in Chemical Graph Theory

“…As an example, matrix A is the adjacency matrix of the chemical graph of 1,2-difluoroethylene (Figure , top), matrix A ‘ is the adjacency matrix for the chemical pseudograph of 1,2-difluoroethylene (Figure , bottom), and matrix D is the distance matrix of both the chemical and general graph of 1,2 difluoroethylene, The sum of the elements either along a row or along a column in A and A ‘ is the degree of a vertex of a chemical graph and pseudograph, respectively, normally called δ and δ ν (valence delta) in molecular connectivity theory . From any chemical graph, and especially from the corresponding adjacency and distance matrices, it is possible to derive a set of topological indices or graph-theoretical indices . ,− The topological indices are numerical quantities which are based on certain topological features of a chemical graph, and they attempt to express numerically, in a direct manner, the topological information content for a given chemical compound. These indices are referred to as graph invariants , since isomorphic graphs possess identical topological indices.…”

Statistical-Mechanical Theory of Topological Indices

“…A networks is a graph G = (V , E) with #V = n nodes (vertices) representing the entities of the system and #E = m edges representing the interactions between pairs of entities [2]. In this context the use of graphs to represent molecules has a long history dating back to the development of graph theory as a discipline [4]. A molecular graph is a graph in which the nodes represent atoms and the edges represent covalent bonds between pairs of atoms in a molecule [5,6].…”

Breadth-First Search Approach to Enumeration of Tree-Like Chemical Compounds

“…It is to be noted that molecular enumeration has also been used as an engine of data mining and knowledge discovery from chemical compound data 3,9,12 . Since the first system for enumerating molecules, DENDRAL 15 came out, more researchers in academia have focused on developing computer-aided technology to study this crucial problem. Approaches for enumerating molecules are based on the representation of chemical compounds as molecular graphs.…”