In this paper, some applications of our earlier results in working with chemical graphs are presented.

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

In chemistry it has been a long established practice to represent molecules by graphs, with the constituent atoms and the interconnecting bonds taking the roles of vertices and edges, respectively. Whereas such representations contain a great amount of chemical information, and are of considerable value, nonetheless, they are in general insufficient to account for energy differences between var...

Graph theory for chemical compounds is often studied for the fact that labeled graphs are suited to express the connectivity of chemical compounds [4]. However, in the field of chemoinformatics, methods using graph algorithms have not entered the mainstream because graph problems comparing two graphs are often intractable. For example, the problem of finding the maximum common subgraph of two g...

Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new algorithm for computing the detour index of molecular graphs is presented. We apply our algorithm on copper and silver nanoclusters ...

A nut graph is a graph on at least 2 vertices whose adjacency matrix has nullity 1 and for which non-trivial kernel vectors do not contain a zero. Chemical graphs are connected, with maximum degree at most three. We present a new algorithm for the exhaustive generation of non-isomorphic nut graphs. Using this algorithm, we determined all nut graphs up to 13 vertices and all chemical nut graphs ...

In order to make sense of biological processes taking part on a cellular level, it is crucial to understand the underlying chemical reactions. In recent years, graph theory has emerged as one of the most approachable and fruitful methods for analysing chemical reaction networks (CRNs). Graph theory can deal with models for which other techniques fail, for example, models where there is incomple...

Computing an invariant of a graph such as treewidth and pathwidth is one of the fundamental problems in graph algorithms. In general, determining the pathwidth of a graph is NP-hard. In this paper, we propose several reduction methods for decreasing the instance size without changing the pathwidth, and implemented the methods together with an exact algorithm for computing pathwidth of graphs. O...

A graph grammar is a generative description of a graph language (a possibly infinite set of graphs). In this paper, we present a novel algorithm for inducing a graph grammar from a given set of ‘positive’ and ‘negative’ graphs. The algorithm is guaranteed to produce a grammar that can generate all of the positive and none of the negative input graphs. Driven by a heuristic specific-to-general s...