Narrow Results

Modeling and computation of molecular descriptors play a crucial role in understanding the properties and characteristics of novel materials like $\gamma$-graphyne, the next-generation wonder material. Triangular $\gamma$-graphyne is an intriguing two-dimensional carbon-based material with diverse potential applications due to its unique electronic, mechanical, and thermal properties. Triangular $\gamma$-graphyne, a distinctive form of carbon allotrope, has garnered substantial interest as a result of its extraordinary characteristics. The notable value lies in its ability to be utilized in diverse domains for potential applications. The interconnected mesh structure of Triangular $\gamma$-graphyne exhibits exceptional mechanical strength and exceptional electron-transporting properties. This makes it a promising material for the development of high-performance electronic devices, such as transistors and sensors. Furthermore, gamma graphyne possesses excellent thermal stability, which makes it suitable for applications in the field of energy storage and conversion. It has the potential to be used as a catalyst in fuel cells or as an electrode material in supercapacitors. In this study, we utilize graph theory to dissect the molecular structure of triangular $\gamma$-graphyne, leading to the derivation of specific mathematical formulas for essential degree-based molecular characteristics. These findings can be instrumental in examining the correlations between the structure and properties of $\gamma$-graphyne. This paper focuses on two structures made from hexagonal honeycomb graphite lattices, like triangular $\gamma$-graphyne and triangular $\gamma$-graphyne chains with respect to some degree-based topological indices. The results obtained will aid in the investigation of the structure-property relationships in $\gamma$-graphyne.

Polymers, either natural or synthetic, permeate all aspects of everyday life. Synthetic compounds such as bakelite, polymethyl methacrylate (acrylic) and vulcanite are commonly used as a foundation for dental prosthetic materials because of their promising properties. [M. Ahmad, M. Saeed and M. Javaid, Comparative study of certain synthetic polymers via bond-additive invariants, IEEE Access9 (2021) 15388–15403] provided a comparative analysis of the aforementioned polymers using significant bond additive invariants. The subdivided line graphs of the aforementioned polymeric structures are fascinating and intricate networks representing new promising molecules. 2D Molecular descriptors (MD) or topological indices are numeric quantities that carry encrypted information about molecular graphs. In this paper, we drive formulas of several molecular descriptors from M-polynomial and generalized Zagreb index for line graphs of the subdivided molecular graph of polymers under discussion. Moreover, we compute ${\text{ABC}}_4$, ${\text{GA}}_5$, and the Sanskruti index for the aforesaid graphs. Finally, we compare various MDs to provide some insight and relation regarding the eminent properties of underlying structures.

The purpose of this paper is to discuss the use of topological indices (TIs) to anticipate the physical and biological aspects of innovative drugs used in the treatment of Alzheimer’s disease. Degree-based topological indices are generated using edge partitioning to assess the drugs Tacrine, Donepezil, Ravistigmine, Butein, Licochalcone-A and Flavokqwain-A. Furthermore, using linear regression, a quantitative structure–property relationship (QSPR) model is developed to predict the characteristics such as boiling point (BP), flash point (FP), molar volume (MV), molecular weight, complexity and polarizability. The findings show that topological indices have the potential to be used as a tool for drugs discovery and design in the field of Alzheimer’s disease treatment.

Chemical graph theory plays an essential role in modeling and designing any chemical structure or chemical network. For a (molecular) graph, the Zagreb indices and the Zagreb eccentricity indices are well-known topological indices to describe the structure of a molecule or graph and can be used to predict properties such as the size and number of rings in a molecule, as well as the thermodynamic stability and reactivity of compounds. In this paper, we introduce a class of molecular models, namely, the Vicsek polygon graphs, which extend the traditional Vicsek networks. We compute the Zagreb indices and the Zagreb eccentricity indices of Vicsek polygon graphs by self-similarity and the recurrence relation based on the construction of graphs.

The Wiener index is a topological index defined as the sum of distances between all pairs of vertices in a graph. It was introduced as a structural descriptor for molecular graphs of alkanes, which are trees with vertex degrees of four at the most. The terminal Wiener index is defined as the sum of distances between all pairs of pendent vertices in a graph. In this paper we investigate Wiener and terminal Wiener for graphs derived from certain operations.

The $F$-index of a graph $G$, denoted by $F(G)$, is defined as the sum of weights $d{(u)}^2+d{(v)}^2$ over all edges $uv$ of $G$, where $d(u)$ denotes the degree of a vertex $u$. In this paper, we give sharp upper bounds of the $F$-index (forgotten topological index) over bicyclic graphs, in terms of the order and maximum degree.

In this paper, we present a new index called min–max distance degree index, $\mathrm{{\rm Y}}(G)$ for molecular graphs. It appears that this index correlates well with properties of 33 and 28 nonanes like, energy of formation and density, and its correlation coefficient is 0.812 and 0.754, respectively. The basic mathematical features and graph operations are presented. In addition, the linear regression analysis of predicted and experimental boiling point of acyclic hydrocarbons is shown, where predicted boiling point is determined by implementing this index with Wiener’s model.

Among topological descriptor of graphs, the connectivity indices are very important and they have a prominent role in theoretical chemistry. The atom-bond connectivity index of a connected graph $G$ is represented as $ABC(G)={\sum }_{uv\in E(G)}\sqrt{\frac{d_v+d_u-2}{d_v{d}_u}}$, where $d_v$ represents the degree of a vertex $v$ of $G$ and the eccentric connectivity index of the molecular graph $G$ is represented as $\xi (G)={\sum }_{v\in V}{d}_v𝜀(v)$, where $𝜀(v)$ is the maximum distance between the vertex $v$ and any other vertex $u$ of the graph $G$.

The new eccentric atom-bond connectivity index of any connected graph $G$ is defined as ${ABC}_5(G)={\sum }_{uv\in E(G)}\sqrt{\frac{𝜀(u)+𝜀(v)-2}{𝜀(u)𝜀(v)}}$.

In this paper, we compute the new eccentric atom-bond connectivity index for infinite families of tetra sheets equilateral triangular and rectangular networks.

If $G$ is a simple graph on $n$ vertices $v_1,v_2,\dots ,v_n$ and $d_i$ be the degree of $i$th vertex $v_i$ then the average degree matrix of graph $G$, $\mathrm{\text{AD}}(G)$ is of order $n\times n$ whose $(i,j)$th entry is $\frac{d_i+d_j}{2}$ if the vertices $v_i$ and $v_j$ are adjacent and zero otherwise. The average degree energy of $G$, $\mathrm{\text{AD}}(E(G))$ is the sum of all absolute value of eigenvalues of average degree matrix of a graph $G$. In this paper, bounds for average degree energy $\mathrm{\text{AD}}(E(G))$ and the relation between average degree energy $\mathrm{\text{AD}}(E(G))$ and energy $E(G)$ is discussed.

In this study, we suggest an eccentricity-based linear regression model to predict the effectiveness of anti-Alzheimer’s drugs such as Tacrine, Donepezil, Rivastigmine, Butein, Licochalcone-A and Flavokawain-A. The relationship between structural characteristics and therapeutic effectiveness by integrating eccentricity values is derived from these drugs. Our findings provide promising insights into the potential use of eccentricity-driven linear regression as a drug discovery tool in the field of Alzheimer’s disease treatment. This method provides an improved comprehension of the structural factors influencing drug efficacy, establishing the way for more targeted and efficient anti-Alzheimer’s drug development. Moreover, a quantitative structure–property relationship model is developed by using linear regression model to predict properties such as boiling point, flash point, molar volume, molecular weight, complexity and polarizability.