Search Results (23)

The aim of this study was to prevent the development of microorganisms in the refrigerated storage of tench by releasing allyl isothiocyanate (AITC) produced by black mustard seeds. Tench reared in an aquaculture centre were sacrificed and the fillets were separated. Different amounts of defatted mustard seed (300, 400 and 500 mg) were added to hermetic polypropylene trays. Microbiological, sensory, and gas chromatography with MS detection analysis were done. AITC release increased progressively until the third day of storage, significantly delaying the development of microorganisms in samples with higher mustard seed content. The tasting panel detected positive aromas at the beginning of the study, but these decreased and negative aromas appeared. The mustard seed treatment resulted in a higher positive aroma at the end of the storage, reducing rotting and ammonia odours. A total of 31 volatile compounds were detected and grouped into hydrocarbon, alcohol, benzenoid, isothiocyanate, ketone, acetate, aldehyde, and others. Butylated hydroxytoluene, an indicator of bacterial contamination, was the major aromatic compound found during storage. The release of AITC resulted in fewer organic compounds with negative aromas appearing during storage. PCA analysis allowed us to classify the assays during storage according to their volatile profiles, confirming the differences observed between treatments. Thus, adding mustard seed to fish packaging could be a viable alternative to extending the product’s shelf life and ensuring food safety. Full article

With geometric significance, the Euler Sombor index of a graph $\Gamma$ is defined as $EP(\Gamma )={\sum }_{\left\{uv\right\}\in E(\Gamma )}\sqrt{d{\left(u\right)}^2+d{\left(v\right)}^2+d\left(u\right)d\left(v\right)}$. It originates from the mathematical distance property and has been proven to have good chemical applications in octane isomers. In this paper, the minimum and maximum of the Euler Sombor index for unicyclic graphs with given girth, as well as the corresponding extremal graphs, are determined. As an application, the experimental values of this index for some benzenoid hydrocarbons and drug molecules were compared with the boiling point. Through regression analysis, it was further demonstrated that the Euler Sombor index has excellent predictability in the physicochemical properties of compounds. Full article

Cheminformatics bridges chemistry, computer science, and information technology to predict chemical behaviors using quantitative structure–property relationships (QSPRs). This study advances QSPR modeling by introducing novel connection-based graphical invariants, specifically designed to enhance the predictive accuracy for physicochemical properties (PCPs) of benzenoid hydrocarbons (BHs). Employing cutting-edge computational methods, we evaluate these invariants against established descriptors in modeling the normal boiling point and standard heat of formation. The findings reveal superior predictive performance by newly proposed invariants, such as the sum-connectivity connection index, outperforming traditional indices like the Zagreb connection indices. Furthermore, we extend these methods to model the physicochemical properties of coumarin-related anti-cancer drugs, demonstrating their potential in drug development. The statistical analysis suggests that the most appropriate structure–property models are nonlinear. This work not only proposes robust tools for PCP estimation but also advocates for rigorous testing of descriptors to ensure relevance in cheminformatics. Full article

Topological indices are numerical invariants derived from graph structures that are essential tools used in computational chemistry and biology for encoding molecular information. By exploiting the inherent symmetries of molecular graphs, we develop efficient algorithms to compute these indices, particularly for large and complex molecules. These indices are rooted in vertex degrees, edge degrees, and other graph parameters, have been extensively studied, and are crucial for understanding the relationship between molecular structure and properties. Recent research has focused on the entire Zagreb indices, which integrate both vertex and edge degrees considering adjacency and incidence relationships. This paper introduces a novel variant, namely, the modified forgotten entire Zagreb index. The efficacy of this new index is underscored by its robust correlation with the physical and chemical properties of octane isomers and lower benzenoid hydrocarbons. Additionally, we derive explicit formulas for this index for several significant graph families. Full article

The aim of the present study was to comprehensively analyze and identify the metabolites of different varieties of raw peanut, as well as provide a reference for the utilization of different varieties of peanuts. In this study, three varieties of peanuts, namely ZKH1H, ZKH13H, and CFD, were investigated via ultrahigh-performance liquid chromatography (UPLC) and widely targeted metabolomics methods based on tandem mass spectrometry (MS) and solid-phase microextraction-gas chromatography–mass spectrometry (SPME-GC–MS). In total, 417 nonvolatile and 55 volatile substances were detected. The nonvolatile substances were classified into the following 10 categories: organic acids and derivatives (28.9%); organic oxygen compounds (21.9%); lipids and lipid-like molecules (12.6%); organoheterocyclic compounds (9.9%); nucleosides, nucleotides, and analogues (9.4%); benzenoids (7.8%); phenylpropanoids and polyketides (6.1%); organic nitrogen compounds (2.7%); lignans, neolignans, and related compounds (0.5%); and alkaloids and their derivatives (0.3%). The volatile compounds (VOCs) were classified into the following eight categories: organic oxygen compounds (24.1%); organic cyclic compounds (20.4%); organic nitrogen compounds (13%); organic acids and their derivatives (13%); lipids and lipid-like molecules (11.2%); benzenoids (11.1%); hydrocarbons (3.7%); and homogeneous non-metallic compounds (3.7%). Differentially abundant metabolites among the different peanut varieties (ZKH13H vs. CFD, ZKH1H vs. CFD, and ZKH1H vs. ZKH13H) were investigated via multivariate statistical analyses, which identified 213, 204, and 157 nonvolatile differentially abundant metabolites, respectively, and 12, 11, and 10 volatile differentially abundant metabolites, respectively. KEGG metabolic pathway analyses of the differential non-VOCs revealed that the most significant metabolic pathways among ZKH13H vs. CFD, ZKH1H vs. CFD, and ZKH1H vs. ZKH13H were galactose metabolism, purine metabolism, and aminoacyl-tRNA, while the nitrogen metabolism pathway was identified as a significant metabolic pathway for the VOCs. The present findings provide a theoretical foundation for the development and utilization of these three peanut species, as well as for the breeding of new peanut varieties. Full article

Claude Berge (1987) introduced the concept of k-extendable graphs, wherein any independent set of size k is inherently a constituent of a maximum independent set within a graph $H=(V,E)$. Graphs possessing the property of being 1-extendable are termedas Berge graphs. This introduction gave rise to the notion of well-covered graphs and well-dominated graphs. A graph is categorized as well-covered if each of its maximal independent sets is, in fact, a maximum independent set. Similarly, a graph attains the classification of well-dominated if every minimal dominating set (DS) within it is a minimum dominating set. In alignment with the concept of k-extendable graphs, the framework of $(k,\gamma )$-endowed graphs and symmetric $(k,\gamma )$-endowed graphs are established. In these graphs, each DS of size k encompasses a minimum DS of the graph. In this article, a study of $\gamma$-endowed dominating sets is initiated. Various results providing a deep insight into $\gamma$-endowed dominating sets in graphs such as those characterizing the ones possessing a unique minimum DS are proven. We also introduce and study the symmetric $\gamma$-endowed graphs and minimality of dominating sets in them. In addition, we give a solution to an open problem in the literature. which seeks to find a domination-based parameter that has a correlation coefficient of $\rho >0.9967$ with the total $\pi$-electronic energy of lower benzenoid hydrocarbons. We show that the upper dominating number $\Gamma \left(H\right)$ studied in this paper delivers a strong prediction potential. Full article

For a graph $G=(V_G,E_G)$, a degree-based graphical index $G{I}_d$ takes the general form $G{I}_d={\displaystyle \sum _{xy\in E_G}}\varphi (d_x,d_y)$, where $\varphi$ is a symmetric map and $d_i$ is the degree of $i\in V_G$. For $\alpha \in \mathbb{R}$, if $\varphi ={\left(d_x{d}_y\right)}^{\alpha }$ (resp. $\varphi ={(d_x+d_y)}^{\alpha }$), the index is called the general product-connectivity $R_{\alpha }$ (resp. general sum-connectivity $SC{I}_{\alpha }$) index. In this paper, by formulating an optimization problem, we determine the value(s) of $\alpha$, for which the linear/multiple correlation coefficient of $R_{\alpha }$ and $SC{I}_{\alpha }$ with physicochemical properties of benzenoid hydrocarbons is the strongest. This, in turn, fills some research gaps left by similar studies in this area. Full article

This paper is concerned with the general atom-bond sum-connectivity index $AB{S}_{\gamma }$, which is a generalization of the recently proposed atom-bond sum-connectivity index, where $\gamma$ is any real number. For a connected graph G with more than two vertices, the number $AB{S}_{\gamma }\left(G\right)$ is defined as the sum of ${(1-2{(d_x+d_y)}^{-1})}^{\gamma }$ over all edges $xy$ of the graph G, where $d_x$ and $d_y$ represent the degrees of the vertices x and y of G, respectively. For $-10\le \gamma \le 10$, the significance of $AB{S}_{\gamma }$ is examined on the data set of twenty-five benzenoid hydrocarbons for predicting their enthalpy of formation. It is found that the predictive ability of the index $AB{S}_{\gamma }$ for the selected property of the considered hydrocarbons is comparable to other existing general indices of this type. The effect of the addition of an edge between two non-adjacent vertices of a graph under $AB{S}_{\gamma }$ is also investigated. Furthermore, several extremal results regarding trees, general graphs, and triangle-free graphs of a given number of vertices are proved. Full article

Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees of adjacent vertices in graph $\Omega$ provides the multiplicative first Zagreb index of a graph. In the context of graph theory, the generalized multiplicative first Zagreb index of a graph $\Omega$ is defined as the product of the sum of the $\alpha$th powers of the vertex degrees of $\Omega$, where $\alpha$ is a real number such that $\alpha \ne 0$ and $\alpha \ne 1$. The focus of this work is on the extremal graphs for several classes of graphs including trees, unicyclic, and bicyclic graphs, with respect to the generalized multiplicative first Zagreb index. In the initial step, we identify a set of operations that either increases or decreases the generalized multiplicative first Zagreb index for graphs. We then involve analysis of the generalized multiplicative first Zagreb index achieving sharp bounds by characterizing the maximum or minimum graphs for those classes. We present applications of the generalized multiplicative first Zagreb index ${\Pi }_1^{\alpha }$ for predicting the $\pi$-electronic energy $E_{\pi }\left(\beta \right)$ of benzenoid hydrocarbons. In particular, we answer the question concerning the value of $\alpha$ for which the predictive potential of ${\Pi }_1^{\alpha }$ with $E_{\pi }$ for lower benzenoid hydrocarbons is the strongest. In fact, our statistical analysis delivers that ${\Pi }_1^{\alpha }$ correlates with $E_{\pi }$ of lower benzenoid hydrocarbons with correlation coefficient $\rho =-0.998$, if $\alpha =-0.00496$. In QSPR modeling, the value $\rho =-0.998$ is considered to be considerably significant. Full article

Irregularity indices are graph-theoretic parameters designed to quantify the irregularity in a graph. In this paper, we study the practical applicability of irregularity indices in QSPR modeling of the physicochemical and quantum-theoretic properties of compounds. Our comparative testing shows that the recently introduced $IRA$ index has significant priority in applicability over other irregularity indices. In particular, we show that the correlation potential of the $IRA$ index with certain physicochemical and quantum-theoretic properties such as the enthalpy of formation, boiling point, and $\pi$-electron energies is significant. Our QSPR modeling suggests that the regression models with the aforementioned characteristics such as strong curve fitting are, in fact, linear. Considering this the motivation, the $IRA$ index was studied further, and we provide analytically explicit expressions of the $IRA$ index for certain graph operations and compositions. We conclude the paper by reporting the conclusions, implications, limitations, and future scope of the current study. Full article

Benzenoid hydrocarbons have regular structures, attracting the opportunity to test the structural descriptors of their series. In the present study, we compared information entropy, Wiener indices, topological efficiencies, topological roundness, and symmetries of oligoacenes, phenacenes, and helicenes. We found and discussed the mismatches between the descriptors and the symmetry of benzenoids. Among the studied series, helicenes demonstrate the parity effect when the information entropy and topological roundness form saw-like functions depending on the number of the member, odd or even. According to our quantum chemical calculations, this parity effect has no consequences for such molecular properties as molecular polarizability and frontier molecular orbital energies. Further, we demonstrated that the changes in the structural descriptors upon the chemical reactions of benzenoids could be used for the numerical description of chemical processes. Interestingly, the view of the information entropy reaction profile is similar to the energy profiles of chemical reactions. Herewith, the intermediate chemical compounds have higher information entropy values compared with the initial and final compounds, which reminisce the activation barrier. Full article

Coconut is a tropical fruit whose flesh has high flavor quality and nutritional value; however, the differences between coconut varieties are still unclear. Here, volatiles and non-volatiles were profiled at three ripening stages by HS-SPME/GC-MS and UHPLC-MS/MS in two coconut varieties (Hainan Tall, HT and Green Dwarf, GD). Four metabolite classes of volatiles were associated with good aroma including hydrocarbons, benzenoids, alcohols and esters, and these volatiles were generally higher in GD, especially at 7 and 9 months of coconut growth. Pathway-based metabolomics revealed that flavonols and their derivatives were significantly enriched in HT, and some of these metabolites were key determinants of HT flesh bitterness, including kaempferol 7-O-glucoside, a known bitter metabolite. Despite the overall accumulation of amino acids, including L-alanine, L-serine and L-methionine in GD, comparative metabolomics revealed that HT flesh provides a higher content of vitamins than GD. This study sheds light on the metabolic pathways and key metabolites differentiating the flesh flavor quality and nutritional value among coconut varieties, and reveals the possible mechanisms of flavor formation and regulation in coconut fruits. Full article

In this paper, we introduce some new versions based on the locating vectors named locating indices. In particular, Hyper locating indices, Randić locating index, and Sambor locating index. The exact formulae for these indices of some well-known families of graphs and for the Helm graph are derived. Moreover, we determine the importance of these locating indices for 11 benzenoid hydrocarbons. Furthermore, we show that these new versions of locating indices have a reasonable correlation using linear regression with physicochemical characteristics such as molar entropy, acentric factor, boiling point, complexity, octanol–water partition coefficient, and Kovats retention index. The cases in which good correlations were obtained suggested the validity of the calculated topological indices to be further used to predict the physicochemical properties of much more complicated chemical compounds. Full article

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 network. In computer networks data is transmitted in form of packets between source to destination. Such packet-switched networks rely on routing protocols to select the best path. Configurations of these protocols depends on the network acquirements; that is why one routing protocol might be efficient for one network and may be inefficient for a other. Because some protocols deal with hop-count (number of nodes in the path) while others deal with distance vector. This paper investigates the minimum transmission in two-mode networks. Based on some parameters, we obtained the minimum transmission between the class of all connected n-nodes in bipartite networks. These parameters are helpful to modify or change the path of a given network. Furthermore, by using least squares fit, we discussed some numerical results of the regression model of the boiling point in benzenoid hydrocarbons. The results show that the correlation of the boiling point in benzenoid hydrocarbons of the first Zagreb eccentricity index gives better result as compare to the correlation of second Zagreb eccentricity index. In case of a connected network, the first Zagreb eccentricity index ${\xi }_1(\aleph )$ is defined as the sum of the square of eccentricities of the nodes, and the second Zagreb eccentricity index ${\xi }_2(\aleph )$ is defined as the sum of the product of eccentricities of the adjacent nodes. This article deals with the minimum transmission with respect to ${\xi }_i(\aleph )$, for $i=1,2$ among all n-node extremal bipartite networks with given matching number, diameter, node connectivity and link connectivity. Full article

An irregularity index $IR\left(\mathsf{\Gamma }\right)$ of a graph $\mathsf{\Gamma }$ is a nonnegative numeric quantity (i.e., $IR\left(\mathsf{\Gamma }\right)\ge 0$) such that $IR\left(\mathsf{\Gamma }\right)=0$ iff $\mathsf{\Gamma }$ is a regular graph. In this paper, we show that $IRC$ closely correlates with the normal boiling point $T_{bp}$ and the standard heat of formation $\Delta H_f^o$ of lower benzenoid hydrocarbons. The correlation models that fit the data efficiently for both $T_{bp}$ and $\Delta H_f^o$ are linear. We develop further mathematical properties of $IRC$ by calculating its exact expressions for the recently introduced transformation graphs as well as certain derived graphs, such as the total graph, semi-total point graph, subdivision graph, semi-total line graph, double, strong double, and extended double cover graphs. Some open problems are proposed for further research on the $IRC$ index of graphs. Full article