Strong arcs in fuzzy graphs

Objectives: To introduce a contemporary aspect notorious as upper g-eccentric point set, upper g-eccentric number, upper g-eccentric dominating set, upper g-eccentric domination number in fuzzy graphs and related concepts. Methods: Strong arc in fuzzy graphs concepts are used to find upper g-eccentric number and upper g-eccentric domination number. Findings: The new idea upper g-eccentric domination in fuzzy graphs will leads to numerous application such as cell phone tower formation in remote areas. Novelty: Using the concepts g-distance, geodesics and strong arc in fuzzy graphs, the upper g-eccentric dominating set and upper g-eccentric domination number in fuzzy graphs are obtained. Some points are observed in this concept and some theorem related to the upper g-eccentric dominant set, its numbers are proved. Keywords: g-Eccentric Dominating Set; g-Eccentric Domination Number; Upper g-Eccentric Domination Number

Types of arcs in a fuzzy graph

In this manuscript, we introduce a few new types of dominations in intuitionistic fuzzy directed graphs (IFDGs) based on different types of strong arcs (SAs). Our work is not only a direct extension of domination in directed fuzzy graphs (DFGs) but also fills the gap that exists in the literature regarding the dominations in different extended forms of fuzzy graphs (FGs). In the beginning, we introduce several types of strong arcs in IFDGs, like semi-β strong arcs, semi-δ strong arcs, etc. Then, we introduce the concepts of domination in IFDGs based on these strong arcs and discuss its various useful characteristics. Moreover, the dominating set (DS), minimal dominating set (MDS), etc., are described with some fascinating results. We also introduce the concept of an independent set in IFDGs and investigate its relations with the DS, minimal independent set (MIS) and MDS. We also provide numerous important characterizations of domination in IFDGs based on minimal and maximal dominating sets. In this context, we discuss the lower and upper dominations of some IFDGs. In addition, we introduce the terms status and structurally equivalent and examine a few relationships with the dominations in IFDGs. Finally, we investigate the most expert (influential) person in the organization by utilizing the concepts of domination in IFGs.

In this paper, a fuzzifying matroid is induced respectively from a fuzzy graph and a fuzzy vector subspace. The concepts of graphic fuzzifying matroid and representable fuzzifying matroid are presented and some properties of them are discussed. In general, a graphic fuzzifying matriod can not be representable over any field. But when a fuzzifying matroid is isomorphic to a fuzzifying cycle matroid which is induced by a fuzzy tree, it is a representable over any field.

In this paper the domination in fuzzy graphs by using strong arcs are generalized and established the domination concept in Cartesian product on standard fuzzy graphs using strong arcs and non strong arcs.

Median graphs represent a unique category of graphs with significant importance in distance-related concepts within graph theory. This paper aims to expand the concept of median graphs into fuzzy graph theory and investigate whether every fuzzy tree belongs to the classification of the fuzzy median graph. Furthermore, this study characterizes the strong edges in a fuzzy graph using median sets. Additionally, the work delves into the impact of removing bridges and cutvertices on a fuzzy median graph. Finally, the paper proposes a novel model rooted in the concept of the fuzzy median graph for deploying wireless sensors, which is meticulously compared with the widely used branch and bound algorithm. The proposed model demonstrates superior performance in significantly reducing the inter-sensor distances.

The concept of domination is introduced within the context of signed fuzzy graphs (signed-FGs), along with examples, as a novel metric to evaluate graph stability under varying conditions. This metric particularly focuses on dominant sets and integrity measures, providing a well-rounded approach to assessing the structural stability of signed- FGs. The necessity of fulfilling the domination integrity condition in evaluating the performance of signed-FGs is highlighted through a discussion on its formulation and an analysis of its upper and lower bounds. An algorithm for identifying strong arcs and classifying them is presented, along with an algorithm for identifying signed fuzzy trees. Furthermore, the role of symmetry in signed-FGs is explored, revealing that symmetrical structures often correspond to higher domination integrity, thus contributing to the improved stability and predictability of the graphs. The paper also establishes important connections with classical graph varieties, such as complete graphs and their variations, demonstrating that changes in domination integrity increase with certain parameters. Additionally, real-life scenarios where these concepts are applicable serve to complement the theoretical results. The case study findings illustrate the significance of domination integrity in practical contexts by emphasizing various instances where it can be determined and utilized. Such instances include identifying independent dominant sets in path and cycle diagrams, as well as estimating the lower bounds of domination integrity in these structures. The estimation of domination integrity using block graph methods is underscored as crucial for enhancing the efficiency of signed-FG applications.

In this study, numerical models were developed with three different core widths and heights, and numerical analyses were performed to investigate the coupled effects of design parameters on stress and structural weight under gravitational prestress. In addition, the design parameters were optimized using the Response Surface Methodology (RSM), and thus core width and height were determined, providing minimum weight and maximum strength. The numerical findings were validated by comparing them to the statistical-based optimization results. On the other hand, thermal pre-stressed structural analyses were performed to assess the effect of the elasticity modulus and thermal expansion coefficients of the adhesives on the structural responses. The current study demonstrated that core width was more effective than core height on stress and deformation responses, and also that ascending core width had an adverse impact on bending stiffness. Furthermore, the optimum core width and height were determined as 5.0042 and 14.844 mm, respectively, using RSM. The maximum stress and weight responses of the sandwich structure with optimal design parameters were also found as 83.455 kPa and 2.2667 g. It was revealed that impacts of core height become more noticeable with larger core widths, and they should not be considered separately.

Development of eugenol loaded cellulose-chitosan based hydrogels; in-vitro and in-vivo evaluation for wound healing

The application of epoxy resins in high temperature and thermal protection fields is limited due to their low decomposition temperature and low carbon residual rate. In this paper, epoxy resin (EP)/quartz fiber (QF) ceramifiable composites were prepared using a prepreg-molding process. The thermal stability, phase change and mechanical properties after high-temperature static ablation and ceramization mechanism of EP/QF ceramifiable composites were investigated. The addition of glass frits and kaolinite ceramic filler dramatically increases the thermal stability of the composites, according to thermogravimetric (TG) studies. The composite has a maximum residual weight of 61.08%. The X-ray diffraction (XRD) results show that the mullite ceramic phase is generated, and a strong quartz diffraction peak appears at 1000 °C. The scanning electron microscope (SEM) and element distribution analyses reveal that the ceramic phase generated inside the material, when the temperature reaches 1000 °C, effectively fills the voids in composites. The composites have a bending strength of 175.37 MPa at room temperature and retain a maximum bending strength of 12.89 MPa after 1000 °C treatment.

In this paper, the notion of cycle connectivity of bipolar fuzzy graphs is introduced. The concept of strong edge, $P$ cut node, $P$-bridge and $\theta$ - evaluation of bipolar fuzzy graphs are studied. The cycle connectivity of bipolar fuzzy trees, bipolar fuzzy cycles and complete bipolar fuzzy graphs are obtained. A condition for complete bipolar fuzzy graphs to have cyclic cut-nodes is obtained.

The increasing growth of urban areas and the rise in infrastructure development activities have put a strain on the availability of land with desirable soil conditions. This has led to the development of several stabilization techniques that can be used to improve the properties of weaker soils for construction. The research presented here explores the impact of inducing randomly oriented alkali-treated areca fibers for stabilization of silty sand soil. A sequence of experiments was carried out on the soil-fiber mixtures to investigate the strength of the soil after stabilization. At increments of 0.2%, the fiber dose varied between 0 – 0.8% of the dry weight of the soil. The tests conducted includes compaction tests, California bearing ratio (CBR), unconfined compression strength (UCS) tests, and unconsolidated undrained (UU) triaxial tests. The results obtained showed a notable increase in the strength of the soil-fiber mixtures. An increase in fiber content was found to increase the OMC (optimum moisture content) values and decrease the MDD (maximum dry unit weight) values. The maximum strength of the soil-fiber mixture was obtained at 0.6% fiber content. This makes it possible to use silty sand soil subgrades for low-volume roads with a traffic of less than 2 million standard axles based on the IITPAVE analysis. In essence, the test findings indicated that the ideal fiber content to be 0.6%. Stabilization of local on-site soils is one of the sustainable practices that can help extend the life of a pavement and lessen the need for more frequent repairs/maintenance.

Physically crosslinked poly(vinyl alcohol)-hydroxyethyl starch blend hydrogel membranes: Synthesis and characterization for biomedical applications

Oxygen distribution in oxidatively stabilized mesophase pitch fiber

Available phosphorus requirements of food-size channel catfish ( Ictalurus punctatus) fed practical diets in ponds