Connection-Based Multiplicative Zagreb Indices of Dendrimer Nanostars

The field of graph theory is broadly growing and playing a remarkable role in cheminformatics, mainly in chemistry and mathematics in developing different chemical structures and their physicochemical properties. Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. Zagreb indices (ZIs) are the most studied TIs. In this paper, we establish general expressions to calculate the connection-based multiplicative ZIs, namely, first multiplicative ZIs, second multiplicative ZIs, third multiplicative ZIs, and fourth multiplicative ZIs, of two renowned dendrimer nanostars. The defined expressions just depend on the step of growth of these dendrimers. Moreover, we have compared our calculated for both type of dendrimers with each other.

Multiplicative Reverse Geometric-Arithmetic Indices and Arithmetic-Geometric of Silicate Network

In mathematical chemistry, geometric-arithmetic and arithmetic-geometric indices are helpful from both theoretical and practical points of view. We defined two new topological indices, multiplicative reverse geometric-arithmetic and arithmetic-geometric indices, and found the same for some silicate networks.

Semiotic thoughts on biological sequence representations

: The deluge of biological sequences ranging from those of proteins, DNA and RNA to genomes has increased the models for their representation, which are further used to contrast those sequences. Here we present a brief bibliometric description of the research area devoted to representation of biological sequences and highlight the semiotic reaches of this process. Finally, we argue that this research area needs further research according to the evolution of mathematical chemistry and its drawbacks are required to be overcome.

Computing the Narumi–Katayama Index and Modified Narumi–Katayama Index of Some Families of Dendrimers and Tetrathiafulvalene

A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In mathematical chemistry, a particular attention is given to degree-based graph invariant. The Narumi–Katayama index and its modified Narumi–Katayama index of a graph G denoted by NK (G) and NK ∗ (G) are equal to the product of the degrees of the vertices of G. In this paper, we calculate the Narumi–Katayama Index and modified Narumi–Katayama index for some families of dendrimers.

Computing Discrete Adriatic Indices of Probabilistic Neural Network

A Topological index is a numeric quantity which characterizes the whole structure of a graph. Adriatic indices are also part of topological indices, mainly it is classified into two namely extended variables and discrete adriatic indices, especially, discrete adriatic indices are analyzed on the testing sets provided by the International Academy of Mathematical Chemistry (IAMC) and it has been shown that they have good presaging substances in many compacts. This contrived attention to compute some discrete adriatic indices of probabilistic neural networks.

Super Fibonacci Graceful Graphs and Fibonacci Cubes

The popularity of Fibonacci cubes is due to their wide range of uses. In mathematical chemistry, this concept is used in the study of hexagonal graphs. In computer science, Fibonacci cubes are interesting from an algorithmic point of view. V. Hsu introduced them in 1993 to simulate the connections of multiprocessor computer networks. He wanted to get graphs with hypercube properties, the order of which is not a power of two. Therefore, the problem of embedding other graphs in Fibonacci cubes is of interest.

Neighborhood M-Polynomial of Crystallographic Structures

The mathematical chemistry is wealthy, having tools such as polynomials and functions that can predict the properties of compounds. The M-polynomial is one of them which yields degree-based topological indices. In this work, we define the neighborhood M-polynomial to obtain neighborhood degree-based topological indices. Further, we compute some neighborhood degree-based topological indices of the face-centered cubic (fcc) lattice and the crystallographic structure of cuprous oxide (〖Cu〗_2 O) using the neighborhood M-polynomial approach. Also, the results are shown graphically.

Degree Sequence of Graph Operator for some Standard Graphs

Topological indices play a very important role in the mathematical chemistry. The topological indices are numerical parameters of a graph. The degree sequence is obtained by considering the set of vertex degree of a graph. Graph operators are the ones which are used to obtain another broader graphs. This paper attempts to find degree sequence of vertex–F join operation of graphs for some standard graphs.

Zagreb-Type Indices of R-Vertex Join and R-Edge Join of Graphs

There are various methods available which are used to search large chemical databases and to predict the physicochemical properties of molecular structures. Using molecular descriptors for this purpose is the simplest of these methods. The Zagreb indices are amongst the oldest molecular descriptors, and their properties have been extensively studied and applied in QSAR/QSPR studies. The Zagreb coindices were recently introduced, attracting the attention of researchers in mathematical chemistry. In this paper, we study Zagreb indices and several other Zagreb-type indices including the general Randić index, sum-connectivity index, F-index, and Zagreb coindices of R-vertex and edge join of two arbitrary graphs.