152 Results Found

A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties. Miličević reformulated the original Zagreb indices...

The difference of Zagreb indices of a graph G is defined as $\Delta \mathrm{M}\left(G\right)={\displaystyle \sum _{u\in V\left(G\right)}}{\left(d\left(u\right)\right)}^2-{\displaystyle \sum _{uv\in E\left(G\right)}}d\left(u\right)d\left(v\right)$, where $d\left(x\right)$ denotes the degree of a vertex x in G. A Halin graph G is a graph that results from a plane tree T without ver...

Root-indices of graphs are mathematical tools that help us to understand complex systems, like molecules and networks, by capturing key structural information. In this study, we introduce two new root-indices, the first and the second Zagreb root-ind...

The study of the maximum and minimal characteristics of graphs is the focus of the significant field of mathematics known as extreme graph theory. Finding the biggest or smallest graphs that meet specified criteria is the main goal of this discipline...

A topological index as a graph parameter was obtained mathematically from the graph’s topological structure. These indices are useful for measuring the various chemical characteristics of chemical compounds in the chemical graph theory. The num...

A graph is a tool for designing a system’s required interconnection network. The topology of such networks determines their compatibility. For the first time, in this work we construct subdivided ${\eta }^{\zeta }$ network $S\left({\eta }^{\zeta }\mathsf{\Gamma }\right)$ and di...

Graph theory can be used to optimize interconnection network systems. The compatibility of such networks mainly depends on their topology. Topological indices may characterize the topology of such networks. In this work, we studied a symmetric networ...

Given a (molecular) graph, the first multiplicative Zagreb index ${\Pi }_1$ is considered to be the product of squares of the degree of its vertices, while the second multiplicative Zagreb index ${\Pi }_2$ is expressed as the product of endve...

Topological indices are numbers related to sub-atomic graphs to allow quantitative structure-movement/property/danger connections. These topological indices correspond to some specific physico-concoction properties such as breaking point, security, s...

The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let $H$ be a simple graph. The first Zagreb eccentricity index ( $E_1\left(H\right)$ ) is defined to be the summation of squares of the eccentricity of vert...

A two-mode network is a type of network in which nodes can be divided into two sets in such a way that links can be established between different types of nodes. The relationship between two separate sets of entities can be modeled as a bipartite net...

We present lower and upper bounds on the general multiplicative Zagreb indices for bicyclic graphs of a given order and number of pendant vertices. Then, we generalize our methods and obtain bounds for the general multiplicative Zagreb indices of tri...

A topological index is a number related to the atomic index that allows quantitative structure–action/property/toxicity connections. All the more vital topological indices correspond to certain physico-concoction properties like breaking point,...

The reformulated Zagreb indices of a graph are obtained from the classical Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of the end vertices of the edge minus 2. In this paper...

Let R be a commutative ring with identity, and $Z\left(R\right)$ be the set of zero-divisors of R. The weakly zero-divisor graph of R denoted by $W\Gamma \left(R\right)$ is an undirected (simple) graph with vertex set $Z{\left(R\right)}^{*}$, and two distinct vertices...

Topological indices are often used to predict the physicochemical properties of molecules. The multiplicative sum Zagreb index is one of the multiplicative versions of the Zagreb indices, which belong to the class of most-examined topological indices...

The variable Zagreb ^vM₂ index is introduced and applied to the structure-boiling point modeling of benzenoid hydrocarbons. The linear model obtained (thestandard error of estimate for the fit model S_fit=6.8 ^oC) is much better than thecorresponding mo...

Based on picture fuzzy sets (PFSs), we use a mathematical model to tackle such types of problems when a person has opinions like yes, no, abstain, and refusal. The spherical fuzzy model is more flexible and practical than the picture fuzzy model, as...

Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the iso...

Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a...

A chemical graph is an illustration of a chemical compound’s structural formula, where the edges indicate covalent bonding and the vertices depict atoms. In the study of (molecular) graphs, Zagreb indices and their variations are the most studi...

There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physica...

A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices $A_{\alpha }$ and $B_{\alpha }$, defined...

The field of mathematics that studies the relationship between algebraic structures and graphs is known as algebraic graph theory. It incorporates concepts from graph theory, which examines the characteristics and topology of graphs, with those from...

Topological indices are useful for predicting the physicochemical behavior of chemical compounds. A main problem in this topic is finding good bounds for the indices, usually when some parameters of the graph are known. The aim of this paper is to us...

The utilizations of graph theory in chemistry and in the study of molecule structures are more than someone’s expectations, and, lately, it has increased exponentially. In molecular graphs, atoms are denoted by vertices and bonds by edges. In t...

Studies of brain network organisation have swiftly adopted graph theory-based quantitative analysis of complicated networks. Small-world topology, densely connected hubs, and modularity characterise the brain’s structural and functional systems...

Graph theory has much great advances in the field of mathematical chemistry. Chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the num...

The bismuth tri-iodide $(Bi{I}_3)$ is an inorganic compound. It is the result of the response of bismuth and iodine, which has inspired enthusiasm for subjective inorganic investigation. The topological indices are the numerical invariants of...

Face-centered cubic lattice $FCC\left(n\right)$ has received extensive consideration as of late, inferable from its recognized properties and non-poisonous nature, minimal effort, plenitude, and basic creation process. The graph of a face-centered cu...

Entropy is a thermodynamic function used in chemistry to determine the disorder and irregularities of molecules in a specific system or process. It does this by calculating the possible configurations for each molecule. It is applicable to numerous i...

Four pendenticity based topological descriptors termed as superaugmented pendentic indices have been conceptualized in the present study. An in-house computer program was utilized to compute index values of all the possible structures (with at least...

Graph-based molecular structure descriptors (often called “topological indices”) are useful for modeling the physical and chemical properties of molecules, designing pharmacologically active compounds, detecting environmentally hazardous...

Tickysim is a clock tick-based simulator for the inter-chip interconnection network of the SpiNNaker architecture. Network devices such as arbiters, routers, and packet generators store, read, and write forward data through fixed-length FIFO buffers....

Chemical graph theory plays an important role in modeling and designing any chemical structure. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. In this pape...

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices ar...

Entropy is a thermodynamic function in physics that measures the randomness and disorder of molecules in a particular system or process based on the diversity of configurations that molecules might take. Distance-based entropy is used to address a wi...

Chemical descriptors are numeric numbers that capture the whole graph structure and comprise a basic chemical structure. As a topological descriptor, it correlates with certain physical aspects in addition to its chemical representation of underlying...

Shannon entropy, also known as information entropy or entropy, measures the uncertainty or randomness of probability distribution. Entropy is measured in bits, quantifying the average amount of information required to identify an event from the distr...

A VDB (vertex-degree-based) topological index over a set of digraphs $\mathcal{H}$ is a function $\phi :\mathcal{H}\to \mathbb{R}$, defined for each $H\in \mathcal{H}$ as $$\phi \left(H\right)=\frac{1}{2}\sum _{uv\in E}{\phi }_{d_u^{+}{d}_v^{-}},$$ where E is the arc set of H, $d_u^{+}$ and $d_v^{-}$ denote the out-degree and in-de...

In the studies of quantitative structure–activity relationships (QSARs) and quantitative structure–property relationships (QSPRs), graph invariants are used to estimate the biological activities and properties of chemical compounds. In th...

In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs J_n,_m for all values of m and n. From the M-polynomial, we recover many degree-based topological indices such as...

Topological indices collect information from the graph of molecule and help to predict properties of the underlying molecule. Zagreb indices are among the most studied topological indices due to their applications in chemistry. In this paper, we comp...

A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this report, we compu...

Fractals are geometric patterns that appear self-similar across all length scales and are constructed by repeating a single unit on a regular basis. Entropy, as a core thermodynamic function, is an extension based on information theory (such as Shann...

Graph theory is used for modeling, designing, analysis and understanding chemical structures or chemical networks and their properties. The molecular graph is a graph consisting of atoms called vertices and the chemical bond between atoms called edge...

A topological index of a graph is a single numeric quantity which relates the chemical structure with its underlying physical and chemical properties. Topological indices of a nanosheet can help us to understand the properties of the material better....

In this article, we study the chemical graph of a cyclic octahedron structure of dimension n and compute the eccentric connectivity polynomial, the eccentric connectivity index, the total eccentricity, the average eccentricity, the first Zagreb index...

Topological indices and connectivity polynomials are invariants of molecular graphs. These invariants have the tendency of predicting the properties of the molecular structures. The honeycomb network structure is an important type of benzene network....

A topological index, which is a number, is connected to a graph. It is often used in chemometrics, biomedicine, and bioinformatics to anticipate various physicochemical properties and biological activities of compounds. The purpose of this article is...