Wiener Index Research Articles

Study on the Natural Regeneration Characteristics and Influencing Factors of Typical Quercus Forests in Northern China

This study aims to analyze the natural regeneration characteristics and the key factors of Quercus forests, providing a theoretical foundation for maintaining the ecological stability of Quercus forests in northern China. In June and July 2023, 17 square plots of five Quercus species in Beijing were surveyed, and seedling regeneration and environmental factors (site, stand and soil factors) were measured. Pearson correlation and random forest algorithms were used to identify the relevant and key environmental factors affecting seedling regeneration density (Seedling 1, Seedling 2, Seedling 3). The natural regeneration capabilities of the five Quercus species in the Beijing area vary, with Quercus aliena and Quercus variabilis being stronger, while Quercus mongolica, Quercus acutissima and Quercus dentata are relatively weaker. Correlation analysis showed that Seedling 1 has no significant correlation with environmental factors; Seedling 2 is significantly negatively correlated with Pielou’s evenness (J) and exchangeable calcium (ECa) (p < 0.05); Seedling 3 is significantly positively correlated with species richness (S), Shannon–Wiener index (H), stand volume (M), and litter layer thickness (LT) (p < 0.05), and significantly negatively correlated with Pielou’s evenness (J) (p < 0.01). The random forest algorithm indicated that the regeneration of Seedling 1 is mainly affected by stand factors, while the regeneration of Seedling 2 and Seedling 3 is more influenced by soil and site factors. The Quercus forests in the Beijing region exhibit a rich species composition and demonstrate a certain capacity for natural regeneration. However, seedling growth is more constrained by soil and site factors in the later stages. Therefore, in the management of Quercus forests, environmental factors can be regulated during the seedling growth stage to create more suitable conditions for regeneration.

The minimum Wiener index of Halin graphs with characteristic trees of diameter 4

The minimum Wiener index of Halin graphs with characteristic trees of diameter 4

The Wiener Index and the Wiener Complexity of the Zero-Divisor Graph of a Ring

We calculate the Wiener index of the zero-divisor graph of a finite semisimple ring. We also calculate the Wiener complexity of the zero-divisor graph of a finite simple ring and find an upper bound for the Wiener complexity in the semisimple case.

Adjacency spectrum and Wiener index of essential ideal graph of a finite commutative ring

Let R be a commutative ring with unity. The essential ideal graph ER of R, is a graph with a vertex set consisting of all nonzero proper ideals of R and two vertices I and K are adjacent if and only if I + K is an essential ideal. In this paper, we study the adjacency spectrum of the essential ideal graph of the finite commutative ring Zn, for n = {pm, pm1qm2}, where p, q are distinct primes, and m, m1 , m2 ε N. We show that 0 is an eigenvalue of the adjacency matrix of EZn if and only if either n = p2 or n is not a product of distinct primes. We also determine all the eigenvalues of the adjacency matrix of EZn whenever n is a product of three or four distinct primes. Moreover, we calculate the topological indices, namely the Wiener index and hyper-Wiener index of the essential ideal graph of Zn, for different forms of n.

THE NON-COPRIME GRAPHS OF UPPER UNITRIANGULAR MATRIX GROUPS OVER THE RING OF INTEGER MODULO WITH PRIME ORDER AND THEIR TOPOLOGICAL INDICES

In its application graph theory is widely applied in various fields of science, including scheduling, transportation, industry, and structural chemistry, such as topological indexes. The study of graph theory is also widely applied as a form of representation of algebraic structures, including groups. One form of graph representation that has been studied is non-coprime graphs. The upper unitriangular matrix group is a form of group that can be represented in graph form. This group consists of upper unitriangular matrices, which are a special form of upper triangular matrix with entries in a ring R and all main diagonal entries have a value of one. In this research, we look for the form of a non-coprime graph from the upper unitriangular matrix group over a ring of prime modulo integers and several topological indexes, namely the Harmonic index, Wiener index, Harary index, and First Zagreb index. The findings of this research indicate that the structure of the graph and the general formula for the Harmonic index, Wiener index, Harary index, and First Zagreb index were successfully obtained.

Seasonal Dynamics and Environmental Drivers of Phytoplankton in the Albufera Coastal Lagoon (Valencia, Spain)

The Albufera of Valencia is a hypereutrophic, oligohaline lagoon that has experienced significant changes in phytoplankton composition and state in recent decades due to human activities. These activities affect phytoplankton biomass and community structure, which are key indicators of ecosystem health. In this study, phytoplankton samples from the lagoon were analyzed to identify dominant groups and genera, and their seasonal cycles were determined using biovolume measurements with the Utermöhl method. Various environmental variables were also measured. Diversity was assessed using richness, equitability, and the Shannon–Wiener index. Canonical Correspondence Analysis (CCA) and Pearson correlation revealed that temperature and phosphorus significantly influence phytoplankton abundance. A species that exhibited seasonal abundance, resulting in a change in the lagoon’s color from green to brown, was identified. Water quality was assessed using the trophic state index, indicating that the lagoon is in poor condition and hyper-eutrophic. Cyanobacteria were the most dominant group, peaking in November, contrary to previous studies, followed by Chlorophyceae and Bacillariophyceae. Phytoplankton are vital bioindicators for assessing ecosystem health, underscoring the need for further research in this area.

Five Years of Natural Vegetation Recovery in Three Forests of Karst Graben Area and Its Effects on Plant Diversity and Soil Properties

In recent decades, excessive human activities have led to large-scale rocky desertification in karst areas. Vegetation restoration is one of the most important ways to control rocky desertification. In this study, vegetation surveys were conducted on three typical plantations in Jianshui County, Yunnan Province, a typical karst fault basin area, in 2016 and 2021. The plantations were Pinus massoniana forest (PM), Pinus yunnanensis forest (PY), and mixed forests of Pinus yunnanensis and Quercus variabilis (MF). Plant diversity and soil nutrients were compared during the five-year period. This paper mainly draws the following results: The plant diversity of PM, PY, and MF increased. With the increase of time, new species appeared in the tree layer, shrub layer, and herb layer of the three forests. Tree species with smaller importance values gradually withdrew from the community. In the tree layer, the Patrick index, Simpson index, and Shannon–Wiener index of the three forests increased significantly. The Pielou index changed from the highest for PM in 2016 to the highest for PY in 2021. In the shrub layer, the Pielou index of the three forests increased. The Patrick index changed from the highest for MF in 2016 to the highest for PY in 2021. There was no significant difference in species diversity index for the herb layer. With the increase of vegetation restoration time, the soil bulk density (BD) of the three forests decreased. There was no significant difference in soil total porosity (TP), soil capillary porosity (CP), and non-capillary porosity (NCP). The pH of PM increased significantly from 5.88~6.24 to 7.24~7.34. The pH of PY decreased significantly (p < 0.05). The contents of total nitrogen (TN) and ammonium nitrogen (NH4+-N) in PY and MF decreased. The content of nitrate nitrogen (NO3−-N) in the three forests increased significantly (p < 0.05). Total phosphorus (TP) content decreased in PM and MF. The content of available phosphorus (AP) in PM and PY increased. In general, with the increase of vegetation restoration time, plant diversity and soil physical and chemical properties have also been significantly improved. The results can provide important data support for vegetation restoration in karst areas.

Assessing the Black Sea Mesozooplankton Community Following the Nova Kakhovka Dam Breach

In June 2023, following the breach of the Nova Kakhovka Dam during the Ukraine-Russia war, a comprehensive study was conducted along the Romanian Black Sea coast to assess water quality and mesozooplankton communities. Surface water analyses revealed significant gradients in nutrient levels and salinity, particularly from north to south, influenced by the influx of freshwater and nutrients from riverine sources and the dam breach. Flooding was found to significantly impact nutrient dynamics and species distributions, with increased concentrations of SiO4 and NO3 in flooded stations. A strong relationship was observed between environmental factors and biological assemblages, with silicates identified as a key driver. Biodiversity patterns varied across regions, with the Shannon–Wiener Index indicating lower zooplankton diversity in transitional waters, reflecting environmental stress. Statistical methods, including correlation analysis, multidimensional scaling, t-tests, and canonical analysis, were employed to investigate the links between mesozooplankton communities and environmental variables. These findings underscore disruptions in trophic dynamics and ecosystem balance, emphasizing the need for integrated environmental management strategies to mitigate further degradation and foster the ecological recovery of the Black Sea.

Ecohydrological Conditions in Urban Wells and Patterns of Invertebrate Fauna Distribution (Kraków, Poland)

ABSTRACTGroundwaters are threatened by various kinds of contaminants, especially in cities. The results of an ecohydrological analysis (hydrobiological, chemical and geological) conducted in 91 urban wells in Kraków showed their effect on fauna composition and abundance. In 74 wells, the presence of invertebrates, chiefly characteristic for surface water, as well as Collembola was stated. Copepoda were found in 40 wells, whereas Nematoda, Annelida and Diptera larvae were found at over a dozen sites. Microturbellaria, Rotifera, Ostracoda and Amphipoda were present in only a few wells. The aim of this article was to find the patterns of invertebrates' distribution in the wells to further understanding of their relationships with groundwater chemistry and the geological background. This is especially important in light of the anthropogenic pollution occurring in wells and the desired attainment of the good ecological status of groundwater. According to Student's t‐test, the presence of fauna did not depend on the studied environmental factors, whereas Pearson correlations showed that total fauna abundance and Copepoda occurrence positively correlated with water temperature which was higher in the city in comparison to that in rural wells. The value of the Shannon–Wiener index and the number of taxa negatively correlated with the well's depth. High variations of water chemical parameters caused by mixed lithology and hydrogeology as well as spotty contamination may affect the occurrence of fauna.

Effect of Environmental Variables on Plant Community Formation and Vegetation Dynamics in Northwest Ethiopia

Identifying plant communities has been a central aspect of vegetation science for centuries, with emphasis on the distribution, composition, and classification of plant communities. This study aimed to assess how environmental variables influence plant community formation and vegetation dynamics in northwest Ethiopia. A systematic random sampling technique was employed to gather vegetation data from 50 plots, each measuring 20 × 20 m, arranged at 100‐m intervals along seven transects. In each plot, the encountered species and their percentage cover‐abundance were recorded, which were subsequently transformed into a modified Braun–Blanquet scale. Additionally, composite soil samples collected from 15 × 15 cm subplots were analyzed for 20 soil parameters. The Shannon–Wiener index was used to measure species diversity. Hierarchical clustering and ordination analyses (DCA and RDA) were conducted on the floristic and environmental data, respectively, using R software. A total of 69 woody plant species from 64 genera and 44 families were recorded at altitudes ranging from 2485 to 2747 m above sea level. The Shannon–Wiener diversity index (H) was 3.74, and the evenness index (J) was 0.90. These high species diversity indices showed ecosystem health, stability, reflecting effective species interactions, and resource utilization. Among 6 terrain variables and 14 edaphic factors, 12 of these environmental factors (altitude, slope, aspect, cutting, silt, pH, sand, organic carbon, organic matter, total nitrogen, phosphorus, and calcium) were found significantly to (p ≤ 0.05) explain the variation in species composition and community formation of four plant communities in the study area. The observed patterns of community formation underscore the need to design different conservation measures tailored to the specific environmental conditions at different elevations.

On the Edge‐Density of the Brownian Co‐Graphon and Common Ancestors of Pairs in the CRT

ABSTRACTBassino et al. have shown that uniform random co‐graphs (graphs without induced ) of size converge to a certain non‐deterministic graphon. The edge density of this graphon is a random variable whose first moments have been computed by these authors. The first purpose of this note is to observe that, in fact, these moments can be computed by a simple recurrence relation. The problem leads us to the following question of independent interest: given i.i.d. uniform pairs of points , in the Brownian CRT, what is the size of the set formed by their pairwise last common ancestors? We show that in probability, with . The method to establish the recurrence relation is reminiscent of Janson's computation of moments of the Wiener index of (large) random trees. The logarithm factor in the convergence result comes from the estimation of Riemann sums in which summands are weighted by the integer divisor function—such sums naturally occur in the problem. We have not been able to analyze the asymptotics of moments of directly from the recurrence relation, and in fact our study of is independent from it. Several things remain to be done; in particular, we only scratch the question of large deviations of , and the precise asymptotics of moments of is left open.

Mite diversity of cupuaçu trees (Theobroma grandiflorum: Malvaceae) in the state of Pará, Amazon, Brazil

ABSTRACT The aim of this study was to identify the mite fauna associated with cupuaçu plantations in Bragança and Augusto Corrêa, Pará, Brazil. In order to investigate the variability and composition of these organisms in cupuaçu plantations in two different locations, systematic collections were carried out at specific times throughout two periods. In addition to mite collection, environmental data such as temperature, relative humidity, atmospheric pressure and precipitation were recorded. Statistical data were obtained through sampling effort and diversity, Hill’s diversity profile and nonmetric multidimensional scaling (NMDS). A total of 868 mites belonging to 53 species were sampled. Seventeen families/suborders of mites were identified, the five most abundant being: Eriophyidae (44.7%), Phytoseiidae (21.1%), Cunaxidae (9%), Oribatida (5.5%) and Tenuipalpidae (3.5%). The data indicated a greater number of mites sampled during the rainy season compared to the dry season, representing approximately 90% more mites in the rainy season. Greater richness was observed during the dry season, with 38 taxa identified. Bragança contributed a total of 551 individuals, while Augusto Corrêa recorded 317 mites. For the Shannon- Wiener index, the municipalities presented similar diversity. Therefore, we highlight the importance of these results for understanding the mite community associated with cupuaçu trees.

Community characteristics of macrobenthos and ecosystem health assessment in ten reservoirs of Henan Province, China

Assessing the eco-health of regional reservoirs is essential for sustainable water resource utilization and water security, particularly in water-scarce areas. This study constructed a Benthic Index of Biotic Integrity (B-IBI) based on the community characteristics of macrobenthos in ten large and medium-sized reservoirs across four major river basins in Henan Province, China. A total of 90 taxa were identified, representing 3 phyla, 6 classes, 17 orders, 45 families and 81 genera. The B-IBI was derived from five key metrics: the number of crustacean and mollusca taxa, Intolerant %, the BI index, the BMWP index, and the Shannon–Wiener index. The B-IBI scores across 44 sites in the ten reservoirs ranged from 0.35 to 3.99. The assessment classified two reservoirs (QTH and HKC in the Yellow River basin) as poor, whereas one reservoir (QP in the Huai River sbasin) was classified as excellent. The B-IBI index effectively distinguished impaired sites from reference sites, supporting its suitability for eco-health assessments of reservoirs in Henan Province.

Spatial and Seasonal Dynamics of Plankton Community and Its Relationship with Environmental Factors in an Urban River: A Case Study of Wuxi City, China

To explore how environmental factors affect the structure of plankton in urban rivers, we analyzed the Caowangjing River, an urban river that passes through Wuxi, to survey the water environmental factors and plankton population in different seasons. We identified 103 phytoplankton species belonging to eight phyla, with Chlorophyta, Bacillariophyta, and Cyanobacteria being the dominant groups. A total of 45 zooplankton species belonged to three classes, with Rotifera being the dominant class. Phytoplankton density was highest in the autumn, followed by the spring, and the lowest in the summer. Phytoplankton biomass, along with zooplankton density and biomass, exhibited seasonal declines. The average values of the Shannon–Wiener index, Pielou’s evenness index, and Margalef richness index were 3.58 ± 0.50, 0.72 ± 0.76, and 2.03 ± 0.31, respectively, indicating the Caowangjing River was mildly polluted based on a water quality evaluation. Redundancy analysis showed that turbidity, water temperature, and ammonia nitrogen are the key factors of phytoplankton community distribution, while water temperature, the permanganate index, and ammonia nitrogen are the key factors of zooplankton community distribution.

Biodiversity of Non-Apis Bees (Hymenoptera: Apoidea) in the Potohar Region of Pakistan

Bees are essential for providing ecosystem services such as pollination to many crops worldwide. However, there is growing concern over the decline of bee populations, which threatens agricultural productivity. Despite the known importance of bees, including non-Apis bees, in crop pollination, their diversity and distribution remain understudied in the Potohar region of Pakistan. The current study addresses this gap by assessing the biodiversity of non-Apis bees across five districts of the Potohar region, Pakistan: Attock, Chakwal, Jhelum, Rawalpindi, and Islamabad. The objective was to evaluate the species richness, diversity, and evenness using various richness and diversity indices. A total of 2005 specimens, representing 27 species from 13 genera and five families (Apidae, Halictidae, Colletidae, Megachilidae, and Andrenidae), were collected over 24 surveys conducted between 2012 and 2015. Two richness indices, Shannon’s Species Richness Index and Margalef’s Richness Index, showed moderate to high species richness across localities, with values ranging from 2.378 to 4.186 and 1.508 to 2.711, respectively. Simpson’s Index and Simpson’s Reciprocal Index exhibited dominance and high diversity across sites, with values ranging from 0.094 to 0.880 and 4.446 to 11.315, respectively. Additionally, the Shannon–Wiener and Shannon Equitability indices indicated fairly even species distributions across localities. A correlation analysis revealed strong positive relationships between most indices, except for Simpson’s Reciprocal Index, which showed negative correlations with the other indices. These findings provide crucial insights into the biodiversity of non-Apis bees in the Potohar region and underscore the importance of maintaining diverse pollinator communities to support sustainable agriculture in the area.

A Reduction Analysis of the Weiner Index on Predicting the Boiling Point of Hydrocarbons Using Graph Technique

A Reduction Analysis of the Weiner Index on Predicting the Boiling Point of Hydrocarbons Using Graph Technique

Topological Indices of Inverse Graph for Generalized Quaternion Group

In this paper, some of the famous and known topological indices for the inverse graph of Generalized quaternion group, including: Hosoya polynomial, Wiener index, hyper-Wiener index, first Zagreb index, second Zagreb index, ABC index, eccentric index, eccentric-connectivity index, total eccentric index, first Zagreb eccentric index, second Zagreb Eccentric index, graph energy index, and Estrada index.

Computation of Distance Matrices of Primary Subgraphs

The graph-theoretical (topological) distance matrices and their invariants (polynomials, spectra and wiener numbers) are presented. Use of distance matrix and its invariants in chemistry is surveyed. Method used to compute distance polynomials is Le Verrier-Faddeev-Frame method.Along with this, Wiener numbers are computed. Some new results are presented.

Quantitative Structure-activity Relationship (QSAR) Modelling of Indomethacin Derivatives using Regression Analysis.

Indomethacin is a non-steroidal anti-inflammatory drug (NSAID) used for medication to reduce fever, spondylitis, or shoulder pain. It mainly works by the inhibition of prostaglandins, the endogenous signaling molecules. Fifteen indomethacin derivatives have been analyzed in relation to their physicochemical and molecular properties. Two-dimensional (2D) structures of fifteen indomethacin derivatives were drawn using the ACD Lab Chem Sketch version. Most of the topological parameters, such as wiener index (W), mean wiener index (Wa), Balaban indices (J), Balaban centric index (BAC), and molecular connectivity (χ), were calculated by using E Dragon software. The most common molecular file formats accepted in EDragon software were SMILES notations created online by Babel software and 2D structures of various derivatives, which were converted into 3D optimized structures using online CORINA, provided by Molecular Networks GMBH. 3D structures of compounds were also drawn on Gauss View software for calculations of various density functional theory (DFT) based quantum chemical descriptors, such as total energy (TE), softness (S), hardness (η), chemical potential (μ), highest occupied molecular orbital energy (HOMO), and lowest unoccupied molecular orbital energy (LUMO). All species were fully optimized in the gas phase with a 6-31+G* basis set. The harmonic vibrational frequency calculations were used to confirm that the optimized structures were minima, as characterized by positive vibrational frequencies. Combinations of various descriptors, such as D, ID, IOR, Log P, Mr, Mv, Mw, Pc, BAC, Pz, St, W, Wa, 0χ, 1χ, 2χ,3χ,4χ, 5χ, and Xeq have been found to be significant for modeling of activity. QSAR model no. 2: pIC50= -20.605 (±6.600) IOR - 0.747 (±0.454) I1 -5.083 (±3.478) Xeq + 51.647 optimized with empirical parameters with high statistical quality (R= 0.921, R2=0.848) was found to be the best model obtained. The QSAR model obtained suggests that substituents with a lesser value of the index of refraction and less electronegative groups were favourable for the activity, whereas indomethacin derivatives with a CH2CH2NHCONH(CH2)3ONO2 group at R1 position were unfavourable for the activity. The results were critically discussed based on regression data and cross-validation techniques. Pogliani factor Q and the results of the LOO (leave-one-out) method confirmed the reliability and predictability of the proposed models that could be highly beneficial for the future designing of new analogues with higher potency.

Molecular descriptors of symmetrically configured carbon nanocones via quotient graph technique

Molecular descriptors of symmetrically configured carbon nanocones via quotient graph technique