An approximation of balanced score in neutrosophic graphs with weak edge weights

Neutrosophic concept is known undirected graph theory to involve with complex logistic networks, not clearly given and unpredictable real life situations, where fuzzy logic malfunctions to model. The transportation objective is to ship all logistic nodes in the network. The logistic network mostly experiences in stable condition, but for some edges found to be volatile. The weight of these erratic edges may vary at random (bridge-lifting/bascule, ad hoc accident on road, traffic condition) In this article, we propose an approximation algorithm for solving minimum spanning tree (MST) of an undirected neutrosophic graphs (UNG), in which the edge weights represent neutrosophic values. The approximation upon the balanced score calculation is introduced for all known configurations in alternative MST. As the result, we further compute decisive threshold value for the weak weights amid minimum cost pre-computation. If the threshold triggers then the proper MST can direct the decision and avoid post-computation. The proposed algorithm is also related to other existing approaches and a numerical analysis is presented.

A Study on Weak Edge Detection of COVID-19’s CT Images Based on Histogram Equalization and Improved Canny Algorithm

The coronavirus disease 2019 (COVID-19) is a substantial threat to people’s lives and health due to its high infectivity and rapid spread. Computed tomography (CT) scan is one of the important auxiliary methods for the clinical diagnosis of COVID-19. However, CT image lesion edge is normally affected by pixels with uneven grayscale and isolated noise, which makes weak edge detection of the COVID-19 lesion more complicated. In order to solve this problem, an edge detection method is proposed, which combines the histogram equalization and the improved Canny algorithm. Specifically, the histogram equalization is applied to enhance image contrast. In the improved Canny algorithm, the median filter, instead of the Gaussian filter, is used to remove the isolated noise points. The K -means algorithm is applied to separate the image background and edge. And the Canny algorithm is improved continuously by combining the mathematical morphology and the maximum between class variance method (OTSU). On selecting four types of lesion images from COVID-CT date set, MSE, MAE, SNR, and the running time are applied to evaluate the performance of the proposed method. The average values of these evaluation indicators are 1.7322, 7.9010, 57.1241, and 5.4887, respectively. Compared with other three methods, these values indicate that the proposed method achieves better result. The experimental results prove that the proposed algorithm can effectively detect the weak edge of the lesion, which is helpful for the diagnosis of COVID-19.

Bandwidth of Graphs Resulting from the Edge Clique Covering Problem

Let $n,k,b$ be integers with $1 \le k-1 \le b \le n$ and let $G_{n,k,b}$ be the graph whose vertices are the $k$-element subsets $X$ of $\{0,\dots,n\}$ with $\mathrm{max}(X)-\mathrm{min}(X) \le b$ and where two such vertices $X,Y$ are joined by an edge if $\mathrm{max}(X \cup Y) - \mathrm{min}(X \cup Y) \le b$. These graphs are generated by applying a transformation to maximal $k$-uniform hypergraphs of bandwidth $b$ that is used to reduce the (weak) edge clique covering problem to a vertex clique covering problem. The bandwidth of $G_{n,k,b}$ is thus the largest possible bandwidth of any transformed $k$-uniform hypergraph of bandwidth $b$. For $b\geq \frac{n+k-1}{2}$, the exact bandwidth of these graphs is determined. Moreover, the bandwidth is determined asymptotically for $b=o(n)$ and for $b$ growing linearly in $n$ with a factor $\beta \in (0,1]$, where for one case only bounds could be found. It is conjectured that the upper bound of this open case is the right asymptotic value.

Connectivity in Hypergraphs

In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of Whitney from graphs to hypergraphs. We find that, while determining a minimum weak vertex cut can be done in polynomial time and is equivalent to finding a minimum vertex cut in the 2-section of the hypergraph in question, determining a minimum strong vertex cut is NP-hard for general hypergraphs. Moreover, the problem of finding minimum strong vertex cuts remains NP-hard when restricted to hypergraphs with maximum edge size at most 3. We also discuss the relationship between strong vertex connectivity and the minimum transversal problem for hypergraphs, showing that there are classes of hypergraphs for which one of the problems is NP-hard, while the other can be solved in polynomial time.

Connected Weak Edge Detour Number of a Graph

Certain general properties of the detour distance, weak edge detour set, connected weak edge detour set, connected weak edge detour number and connected weak edge detour basis of graphs are studied in this paper. Their relationship with the detour diameter is discussed. It is proved that for each pair of integers k and n with 2 <= k <= n, there exists a connected graph G of order n with cdnw(G)=k. It is also proved that for any three positive integers R,D,k such that k >= D and R < D <= 2R, there exists a connected graph G with radD (G) = R, diamD G = D and cdnw(G)=k.

Fast Medical Image Segmentation Using Energy-Based Method

Medical applications became a boon to the healthcare industry. It needs correct and fast segmentation associated with medical images for correct diagnosis. This assures high quality segmentation of medical images victimization. The Level Set Method (LSM) is a capable technique, however the quick process using correct segments remains difficult. The region based models like Active Contours, Globally Optimal Geodesic Active Contours (GOGAC) performs inadequately for intensity irregularity images. During this cardstock, we have a new tendency to propose an improved region based level set model motivated by the geodesic active contour models as well as the Mumford-Shah model. So that you can eliminate the re-initialization process of ancient level set model and removes the will need of computationally high priced re-initialization. Compared using ancient models, our model are sturdier against images using weak edge and intensity irregularity.

Fast Medical Image Segmentation Using Energy-Based Method

Medical applications became a boon to the healthcare industry. It needs correct and fast segmentation associated with medical images for correct diagnosis. This assures high quality segmentation of medical images victimization. The Level Set Method (LSM) is a capable technique, however the quick process using correct segments remains difficult. The region based models like Active Contours, Globally Optimal Geodesic Active Contours (GOGAC) performs inadequately for intensity irregularity images. During this cardstock, we have a new tendency to propose an improved region based level set model motivated by the geodesic active contour models as well as the Mumford-Shah model. So that you can eliminate the re-initialization process of ancient level set model and removes the will need of computationally high priced re-initialization. Compared using ancient models, our model are sturdier against images using weak edge and intensity irregularity.