Strong Domination Index in Fuzzy Graphs

Topological indices play a vital role in the area of graph theory and fuzzy graph (FG) theory. It has wide applications in the areas such as chemical graph theory, mathematical chemistry, etc. Topological indices produce a numerical parameter associated with a graph. Numerous topological indices are studied due to its applications in various fields. In this article a novel idea of domination index in a FG is defined using weight of strong edges. The strong domination degree (SDD) of a vertex u is defined using the weight of minimal strong dominating set (MSDS) containing u. Idea of upper strong domination number, strong irredundance number, strong upper irredundance number, strong independent domination number, and strong independence number are explained and illustrated subsequently. Strong domination index (SDI) of a FG is defined using the SDD of each vertex. The concept is applied on various FGs like complete FG, complete bipartite and r-partite FG, fuzzy tree, fuzzy cycle and fuzzy stars. Inequalities involving the SDD and SDI are obtained. The union and join of FG is also considered in the study. Applications for SDD of a vertex is provided in later sections. An algorithm to obtain a MSDS containing a particular vertex is also discussed in the article

Domination Index in Graphs

The concepts of domination and topological index hold great significance within the realm of graph theory. Therefore, it is pertinent to merge these concepts to derive the domination index of a graph. A novel concept of the domination index is introduced, which utilizes the domination degree of a vertex. The domination degree of a vertex a is defined as the minimum cardinality of a minimal dominating set that includes a. The idea of domination degree and domination index is conducted of graphs like complete graphs, complete bipartite, r partite graphs, cycles, wheels, paths, book graphs, windmill graphs, Kragujevac trees. The study is extended to operation in graphs. Inequalities involving domination degree and already established graph parameters are discussed. An application of domination degree is discussed in facility allocation in a city. Algorithm to find a MDS containing a particular vertex is also discussed in the study

Matching in power graphs of finite groups

Funding: The author Swathi V V acknowledges the support of Council of Scientific and Industrial Research, India (CSIR) (Grant No-09/874(0029)/2018-EMR-I), and DST, Government of India, ‘FIST’ (No.SR/FST /MS-I/2019/40).The power graph P(G) of a finite group G is the undirected simple graph with vertex set G, where two elements are adjacent if one is a power of the other. In this paper, the matching numbers of power graphs of finite groups are investigated. We give upper and lower bounds, and conditions for the power graph of a group to possess a perfect matching. We give a formula for the matching number for any finite nilpotent group. In addition, using some elementary number theory, we show that the matching number of the enhanced power graph Pe(G) of G (in which two elements are adjacent if both are powers of a common element) is equal to that of the power graph of G.Publisher PDFPeer reviewe

Comparing the influence of natural farming on cotton (Gossypium hirsutum) yield and economics with integrated and organic farming

Cotton, a vital global cash crop, influences the economy and sustainability. Natural farming is a cost-effective, eco-friendly method. This study examines Natural Farming's effects on cotton yield and the economics of cotton compared to Integrated and organic farming. Field experiments were conducted during 2021-22 and 2022-23 at Tamil Nadu Agricultural College, Coimbatore. The experiment consisted of eight treatments, laid out in Randomized Block Design and replicated thrice. The treatments consist of control (T1), various Indian Natural farming practices including Beejamirit as a seed treatment, Ghanajeevamirit as basal, Jeevamirit with irrigation water, crop residue mulch, intercroping with pulses (T2 to T5), Organic farming practices (T6), Integrated crop management (ICM) practices with organic pest control (T7) and ICM with chemical pest (T8). The results indicated a significant increase in yield components: sympodial branches plant-1 (12.85 and 13.40), number of squares (29.28 and 31.28), bolls plant-1 (10.74 and 11.32), and boll weight (4.30 and 4.38 g) under Integrated Crop Management practices in 2021-22 and 2022-23, respectively. However, organic farming practices, followed by natural farming practices, were at par with integrated crop management. Integrated crop management practices resulted in significantly higher seed cotton yields (2178 and 2232 kg/ha in 2021-22 and 2022-23, respectively) than organic and natural farming practices with a higher cost of cultivation and a gross return. Complete natural farming outperformed organic and integrated farming in cotton, yielding higher net returns and B: C ratios. This approach holds promise for enhancing yield, economic viability and environmental sustainability in cotton cultivation

Food Choice Motives among the Students of a Dental Institution in Mysore City, India

Background: In pursuit of a more gholistich dentistry and an increasing focus on promoting oral health, dental students are increasingly being trained to take a more active part in health promotion and education. In particular, this incorporates an emphasis on diet and educating people to eat in more healthy ways.Aim: This paper works from the premise that if dental students are toengage in oral health promotion, they will do so more effectively if they have first explored their own food choice motivations. Subjects and Methods: A descriptive, cross.sectional questionnaire study. The food choice questionnaire (FCQ) was distributed to a comparative  group of 1st and 5th year dental students in timetabled lecture slots. The FCQ is a previously validated measure designed to assess ten main factors relevant to peoplesh food choices. The data was analyzed using SPSS version 18.0 (Chicago, IL, USA) using descriptive statistics and  independent sample t-test.Results: Nearly 77% (122/159) students responded. Findings were  analyzed using independent sample t-test. Results indicated statistically significant differences in terms of food choice motivations between male and female students of 1st and 5th year.Conclusion: Awareness and an understanding of the differences in  motivational factors affecting food choice between dental students is important as they are increasingly taught to play an active role in oral health promotion. Keywords: Africa, Food, Oral healt

Comparative Evaluation of Inductively Coupled Plasma–Optical Emission Spectroscopy and Atomic Absorption Spectrophotometry for Determining DTPA-Extractable Micronutrients in Soils

A study was conducted for comparative evaluation of atomic absorption spectrophotometry (AAS) and inductively coupled plasma–optical emission spectroscopy (ICP-OES) for determining extractable zinc (Zn), copper (Cu), manganese (Mn), and iron (Fe) in sixty diverse soil samples having a wide range in pH and organic carbon (C). The results were significantly affected by the method of analysis and soil type but generally did not follow a definite trend. Results for extractable Fe in Alfisol samples were significantly greater when using ICP-OES than AAS; and the results for Zn, Cu, and Mn were not significantly different for the two methods. For Vertisol samples, the results for extractable Cu were significantly greater by ICP-OES than by AAS, whereas extractable Fe and Zn were significantly greater by AAS than by ICP-OES, and the results for Mn were not significantly different for the two methods. The results are discussed relative to soil type and differences in soil organic carbon and pH of the samples used in the study

Greener One-pot Synthesis of Chromeno Oxazin and Oxazin Quinoline Derivatives and their Antibacterial Activity

An efficient green method for the synthesis of oxazino quinoline-2-amine derivatives, oxazino quinoline derivatives and chromeno oxazin-5-one derivatives have been synthesized through cyclization of aromatic aldehyde, ammonium acetate, substituted amides and 8-hydroxy-quinoline or 4-hydroxy coumarin by one-pot condensation method is described. The synthesized compounds are characterized by FT-IR, 1H NMR and MASS spectral techniques and are screened further for biological activities against Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus and Bacillus subtilis using cup plate method and disc diffusion method