The stable marriage problem (SM) and its many variants are extensively-studied combinatorial problems with many practical applications. The n-dimensional stable marriage model is proposed, which is initially motivated by a problem arising from chemical graph theory, and an algorithm is given accordingly. This model solves the zero clustering problem of chemical graph polynomials successfully, w...

The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ ...

Mining chemical compounds in silico has drawn increasing attention from both academia and pharmaceutical industry due to its effectiveness in aiding the drug discovery process. Since graphs are the natural representation for chemical compounds, most of the mining algorithms focus on mining chemical graphs. Chemical graph mining approaches have many applications in the drug discovery process tha...

A chemical graph can be recognized by a numerical number (topological index), algebraic polynomial or any matrix. These numbers and polynomials help to predict many physico-chemical properties of underline chemical compound. In this paper, 1Corresponding author. we compute first and second Zagreb polynomials and multiple Zagreb indices of the Line graphs of Banana tree graph, Firecracker graph ...

Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by $af(G)$. In this paper we consider some specifi...

It is well known that the chemical behavior of a compound is dependent upon the structure of itsmolecules. Quantitative structure – activity relationship (QSAR) studies and quantitative structure –property relationship (QSPR) studies are active areas of chemical research that focus on the nature ofthis dependency. Topological indices are the numerical value associated with chemical constitution...

In past years, topological indices are introduced to measure the characters of chemical molecules. Thus, the study of these topological indices has raised large attention in the field of chemical science, biology science and pharmaceutical science. In this paper, by virtue of molecular structure analysis, we determine the total Szeged index, vertex-edge Wiener index and edge hyper-Wiener index ...

Drugs and chemical compounds are often modeled as graphs in which the each vertex of the graph expresses an atom of molecule and covalent bounds between atoms are represented by the edges between their corresponding vertices. The topological indicators defined over this molecular graph have been shown to be strongly correlated to various chemical properties of the compounds. In this article, by...

It is necessary to generate the automorphism group of a chemical graph in computer-aided structure elucidation. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce...