an acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. the acyclic chromatic index of a graph $g$ denoted by $chi_a '(g)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. the maximum degree in $g$ denoted by $delta(g)$, is the lower bound for $chi_a '(g)$. $p$-cuts introduced in this paper acts as a powerfu...

Fibonacenes (zig-zag unbranched catacondensed benzenoid hydrocarbons) are a class of polycyclic conjugated systems whose molecular graphs possess remarkable properties, often related with the Fibonacci numbers. This article is a review of the chemical graph theory of fibonacenes, with emphasis on their Kekulé–structure–related and Clar–structure–related properties. ————————————————— ∗Supported ...

Increased availability of large repositories of chemical compounds is creating new challenges and opportunities for the application of machine learning methods to problems in computational chemistry and chemical informatics. Because chemical compounds are often represented by the graph of their covalent bonds, machine learning methods in this domain must be capable of processing graphical struc...

The energy of a graph G as chemical concept leading to HMO theory was introduced by Hückel in 1931 and developed into mathematical interpretation many years later when Gutman 1978 gave his famous definition the sum absolute values eigenvalues adjacency matrix G. One general requirements for any topological index is that similar molecules have close TI values, which called smoothness. To explore...

‎In addition to his countless contributions to spectral graph theory‎, some works of Dragos Cvetkovic are concerned with chemical problems‎. These are briefly outlined‎, ‎with emphasis on his collaboration with‎ ‎the present author‎.

The central challenge in automated synthesis planning is to be able generate and predict outcomes of a diverse set chemical reactions. In particular, many cases, the most likely pathway cannot applied due additional constraints, which requires proposing alternative With this mind, we present Molecule Edit Graph Attention Network (MEGAN), an end-to-end encoder–decoder neural model. MEGAN inspire...

the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

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...

the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...