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The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we introduce a new invariant which is named as F-coindex. Here, we study basic mathematical properties and the behavior of the newly introduced F-coindex under several graph operations such as union, join, Cartesian product, composition, tensor product, strong product, corona product, disjunction, symmetric difference of graphs and hence apply our results to find the F-coindex of different chemically interesting molecular graphs and nano-structures.

In the present paper, the connective eccentric matrix CE([??]) for a simple connected graph G is introduced and bounds of spectral radius of CE([??]) are obtained. The notion of connective eccentric energy [??] is also introduced and some upper and lower bounds of [??] are obtained here. Keywords: Topological index, graph eigenvalues, connective eccentric index, connective eccentric matrix, connective eccentric energy. AMS Subject Classification: 05C50, 05C35.

In 2023, Bangladesh became the first country to achieve World Health Organization (WHO) validation of elimination of visceral leishmaniasis as a public health problem, defined as maintenance of annual kala-azar incidence at <1 case per 10,000 population at the subdistrict (upazila) level. The pillars of the programme are early diagnosis and effective treatment, indoor residual insecticide spraying, improved case detection, social mobilization and operational research, and effective disease surveillance. The Bangladesh National Kala-azar Elimination Programme was established in 2008, with introduction of rapid diagnostics and newer treatment modalities in health complexes at sub-district level in the endemic area in 2012–2015, initiation of blanket IRS in affected communities in 2012–2013 and adoption of a digital surveillance system in 2015. All subdistricts achieved and maintained the elimination threshold from 2017 onward. We present documentation of the course of KA elimination in Bangladesh and provide a perspective on the components necessary to maintain current success into the future.

Purpose - Corporate social responsibility (CSR) aims at upholding socio-economic condition of deprived communities prevailing in society as well as bringing profitability for corporate companies themselves. This study investigates to what extent the CSR initiatives of financial institutions in Bangladesh have been able to reach out to deprived communities and support various dimensions of financial inclusion (FI) in the country. Design/methodology/approach - In this study, both supply-side and demand-side data are included and discussed rigorously as tools to cross-check the result. Both qualitative and quantitative data are incorporated, and graphs and tables are used to represent the critical information better. A triangulation of in-depth interviews with secondary data is used to ensure rigor and trustworthiness. The triangulation approach works as a method to verify secondary data by interviewees in this study. Findings - The result shows a positive geographical and demographical penetration of CSR activities, but it does not necessarily bring FI in all cases. This study identifies some key issues that prevail in the current context of Bangladesh, such as usage, distance, quality and cost of financial products. Originality/value - This study makes use of both supply-side and demand-side information and thus explain the reasons behind the involuntary exclusion of financial services.

Objective Interleukin‐10 (IL‐10) is a multifunctional cytokine that exerts both pro‐ and anti‐inflammatory effects on the immune system as well as in the pathogenesis of Guillain–Barré syndrome (GBS). We investigated whether the three common polymorphisms ‐1082 G/A(rs1800896), ‐819 C/T(rs1800871), and ‐592 C/A(rs1800872) in the promoter region of IL‐10 have any influence on the susceptibility, severity, and clinical outcome of GBS. Methods IL‐10 promoter polymorphisms were investigated in 152 patients with GBS and 152 healthy controls from Bangladesh using polymerase chain reaction and restriction fragment length polymorphism (PCR‐RFLP), and allele‐specific oligonucleotide‐PCR (ASO‐PCR). Haplotype patterns and frequencies were analyzed using Heatmaply R‐package, chi‐square, and Fisher's exact test. The serum level of IL‐10 was measured through enzyme‐linked immunosorbent assays. p‐values < 0.05 were considered statistically significant. Results IL‐10 promoter polymorphisms ‐1082 G/A, ‐819 C/T, and ‐592 C/A were not associated with GBS susceptibility. The homozygous ‐819 TT genotype showed a tendency with susceptibility (p = 0.029; pc = 0.08) and was prevalent in axonal variants of GBS compared to demyelinating subtypes and controls (p = 0.042, OR = 8.67, 95% CI = 1.03–72.97; pc = 0.123 and p = 0.005, OR = 4.2, 95% CI = 1.55–11.40; pc = 0.015, respectively). Haplotype analysis revealed 19 patterns of genotypes and high IL‐10 expression haplotype combinations (GCC/GTA, GCC/ATA, and GCC/GCA) may have influence on disease severity (p = 0.026; pc = 0.078). Serum expression of IL‐10 was elevated in GBS patients ([GBS, 12.16 ± 45.71] vs. [HC, 0.65 ± 5.17] pg/mL; p = 0.0027) and varied with disease severity ([severe‐GBS, 15.25 ± 51.72] vs. [mild‐GBS, 3.59 ± 19.79] pg/mL, p = 0.046). Interpretation The ‐819 TT genotypes influence axonal GBS, and high frequency of IL‐10 expression haplotype combination with elevated serum IL‐10 may play an important role in disease severity.

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, we study the behavior of the reformulated first Zagreb index and apply our results to different chemically interesting molecular graphs and nano-structures.

BackgroundAlzheimer’s disease (AD) impacts over 55 million individuals worldwide and remains the leading cause of dementia (60–70% of cases). By 2050, South and Southeast Asia are projected to have an older adult population more than double, bearing a major share of Alzheimer’s disease burden. This will exert a heavy strain on healthcare systems, particularly in resource-limited countries where support and infrastructure are already stretched. Despite this, no review has yet explored the regional epidemiology and associated risk factors in this context. Thus, this study protocol outlines to synthesise prevailing evidence from these densely populated regions, particularly low- and middle-income nations within South and Southeast Asia.MethodsThis review will include studies that reported epidemiological characteristics including prevalence, age of onset, mortality, and risk factors of AD and related dementias comprising in South and Southeast Asian regions. Studies published in any language from inception to date will be extracted from PubMed, Scopus, CINAHL, EMBASE and APA PsycNet, following Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) and Meta-Analysis of Observational Studies in Epidemiology (MOOSE) guidelines. We will also search grey literature sources and screen the reference lists of the articles selected for full-text review to identify additional relevant studies. Observational studies including case–control, cohort, and cross-sectional designs reporting desired outcomes will be included and appraised for quality assessment with the modified Newcastle-Ottawa Scale (mNOS). The included articles will be appraised by two independent reviewers, with a third resolving any conflicts. Pooled estimates of prevalence, age of onset and mortality will be analysed using random effect meta-analysis (REML) model. Associated risk factors, including modifiable and non-modifiable will be narratively synthesised. Forest plots will be used to visualise the findings, and heterogeneity across the included studies will be assessed using the I² and Cochrane’s Q statistics. Potential publication bias will be assessed using a funnel plot along with the Begg’s and Egger’s tests. Sensitivity and subgroup analyses will also be conducted to assess the robustness of pooled estimates and to explore potential sources of heterogeneity. Statistical analysis will be conducted using Rstudio (v.4.3.2) and GraphPad Prism V.9.0.2.Ethics and disseminationsThe systematic review is focused on the analysis of secondary data from published literature; thus, no ethical approval will be needed. The protocol will follow international standard guidelines, findings will be reported in a reputed journal and disseminated through (inter)national conferences, webinars and key stakeholders to inform policy, research and AD management strategies.PROSPERO registration numberCRD 420251047105.

The connective eccentric index of a graph is a topological index involving degrees and eccentricities of vertices of the graph. In this paper, we have studied the connective eccentric index for double graph and double cover. Also we give the connective eccentric index for some graph operations such as joins, symmetric difference, disjunction, and splice of graphs.

In this paper, Genetic Algorithm (GA) is used to find the Maximum Weight Independent Set (MWIS) of a graph. First, MWIS problem is formulated as a 0-1 integer programming optimization problem with linear objective function and a single quadratic constraint. Then GA is implemented with the help of this formulation. Since GA is a heuristic search method, exact solution is not reached in every run. Though the suboptimal solution obtained is very near to the exact one. Computational result comprising an average performance is also presented here.

If the adjacency matrix and the degree matrix of a graph G are A ( G ) and D ( G ) respectively, then for a real number α with 0 ≤ α ≤ 1 , the matrix A α ( G ) = α D ( G ) + ( 1 - α ) A ( G ) is called the A α matrix of G . Since for α = 0 and 1/2, A α ( G ) reduces to the adjacency matrix itself and half of the signless Laplacian matrix respectively, it is a generalization of both the adjacency matrix and the signless Laplacian matrix. In this paper, we deduce an upper bound and some lower bounds of the largest eigenvalue of the A α matrix of a connected graph with girth 5 or more. As a consequence, we get the upper and lower bounds of the largest eigenvalue of the adjacency matrix and that of the signless Laplacian matrix of a connected graph with girth 5 or more. We compare those bounds with some existing bounds for general graphs and show that the obtained bounds are incomparable with the existing bounds.