The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula:     ( ) 2 ( ) uv E G u v u v Q Q Q Q GA G , where Qu is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometric-arithmetic index of Vphenylenic nanotube ar...

Chemical reactions are described by edge relabeling graph transformation rules, in which a substrate chemical graph is transformed into a product chemical graph by breaking existing bonds and creating new bonds between atoms. These edge relabeling graph transformation rules are themselves chemical graphs, where the order of a bond before the chemical reaction is distinguished from the order of ...

Chemical compounds are usually represented as graph structured data in computers. In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes. In particular, we consider the following problems: determining whether two chemical graphs are identical, determining whether one inpu...

the dispersibility of graphene is modeled as a mathematical function of the molecular structure of solvent represented by simplified molecular input-line entry systems (smiles) together with the graph of atomic orbitals (gao). the gao is molecular graph where atomic orbitals e.g. 1s1, 2p4, 3d7 etc., are vertexes of the graph instead of the chemical elements used as the graph vertexes in the tra...

Chemical reactions can be represented as graph transformations. Fundamental concepts that relate organic chemistry to graph rewriting, and an introduction to the SMILES chemical graph specification language are presented. The utility of both deduction and unordered finite rewriting over chemical graphs and chemical graph transformations, is suggested. The authors hope that this paper will provi...

Biochemical pathways, such as metabolic, regulatory, and signal transduction pathways, constitute complex networks of functional and physical interactions between molecular species in the cell. They are represented in a natural way as graphs, with molecules as nodes and processes as arcs. In particular, metabolic pathways are represented as directed graphs, with the substrates, products, and en...

The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...

In mathematical chemistry, a particular attention is given to degree-based graph invariant. The Zagrebpolynomial is one of the degree based polynomials considered in chemical graph theory. A dendrimer isan artificially manufactured or synthesized molecule built up from branched units called monomers. Inthis note, the first, second and third Zagreb poly...