Designing new medical drugs for a specific disease requires extensive analysis of many molecules that have an activity for the disease. The main goal of these extensive analyses is to discover substructures (fragments) that account for the activity of these molecules. Once they are discovered, these fragments are used to understand the structure of new drugs and design new medicines for the dis...

The development of chemical applications of graph theory is reviewed from a personal perspective. Graph-theoretical methods for finding all graphs fulfilling certain mathematical conditions followed by eliminating chemically impossible solutions are equivalent to the ‘Sherlock Holmes principle’. For molecular graphs, this is illustrated by monocyclic aromatic systems and by valence isomers of a...

Recently, topology and graph theory have come together to study graphs embedded in 3-space, (see for example [1 5]). An analysis of the symmetries of spatial graphs is useful in chemistry in determining when a molecular bond graph is chiral (i.e., distinct from its mirror image). We are interested in classifying those graphs whose intrinsic structure is such that no matter how they are embedded...

Given a molecular graph G, the Hosoya index Z(G) of G is defined as the total number of the matchings of the graph. Let Bn denote the set of bicyclic graphs on n vertices. In this paper, the minimal, the second-, the third-, the fourth-, and the fifth-minimal Hosoya indices of bicyclic graphs in the set Bn are characterized.

cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. actually,the origin of this concept came back to richard brualdi's problems that are proposed in cite{braldi}:let $g_n$ and $g'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2 g...

7 We study parallel complexity of signed graphs motivated by the highly 8 complex genetic recombination processes in ciliates. The molecular gene 9 assembly operations have been modeled by operations of signed graphs, 10 i.e., graphs where the edges have a sign + or −. In the optimization prob11 lem for signed graphs one wishes to find the parallel complexity by which 12 the graph can be reduce...

in this paper, the weighted szeged indices of cartesian product and corona product of twoconnected graphs are obtained. using the results obtained here, the weighted szeged indices ofthe hypercube of dimension n, hamming graph, c4 nanotubes, nanotorus, grid, t− fold bristled,sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

let $gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. denote by $upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. in the classes of graphs $gamma_{n,kappa}$ and $upsilon_{n,beta}$, the elements having maximum augmented zagreb index are determined.

The elaboration of methods for defining molecular similarity measures is one of the important fields of modern theoretical chemistry. These measures are used for solving a number of problems of theoretical and computer chemistry, in particular the prediction of properties of chemical compounds. For the construction of any molecular similarity measures molecules are represented as some mathemati...

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 ...