A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). A directed graph is a graph in which edges have orientation. A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex.  For a simple undirected graph G with order n, and let  denotes its complement. Let δ(G), ∆(G) denotes the minimum degree and maximum degree of G respectively. The complement degree polynomial of G is the polynomial CD[G,x]= , where C

This paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed f

Some nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems

Image retrieval is used in searching for images from images database. In this paper, content – based image retrieval (CBIR) using four feature extraction techniques has been achieved. The four techniques are colored histogram features technique, properties features technique, gray level co- occurrence matrix (GLCM) statistical features technique and hybrid technique. The features are extracted from the data base images and query (test) images in order to find the similarity measure. The similarity-based matching is very important in CBIR, so, three types of similarity measure are used, normalized Mahalanobis distance, Euclidean distance and Manhattan distance. A comparison between them has been implemented. From the results, it is conclud

     Internet technology has revolutionized the landscape of communication technologies in the modern era. However, because the internet is open to the public, communication security cannot be guaranteed. As a result, data concealment approaches have been developed to ensure confidential information sharing. Various methods have emerged to achieve the goal of secure data communication via multimedia documents. This study proposes a method, which is both adaptable and imperceptible, for concealing a secret text in a color image. From an adaptivity perspective, image corners are detected using the Harris corner detection algorithm and utilized as anchor points for picking the optimal hiding regions of interest using Bezier curve interp

In this paper two main stages for image classification has been presented. Training stage consists of collecting images of interest, and apply BOVW on these images (features extraction and description using SIFT, and vocabulary generation), while testing stage classifies a new unlabeled image using nearest neighbor classification method for features descriptor. Supervised bag of visual words gives good result that are present clearly in the experimental part where unlabeled images are classified although small number of images are used in the training process.

Groupwise non-rigid image alignment is a difficult non-linear optimization problem involving many parameters and often large datasets. Previous methods have explored various metrics and optimization strategies. Good results have been previously achieved with simple metrics, requiring complex optimization, often with many unintuitive parameters that require careful tuning for each dataset. In this chapter, the problem is restructured to use a simpler, iterative optimization algorithm, with very few free parameters. The warps are refined using an iterative Levenberg-Marquardt minimization to the mean, based on updating the locations of a small number of points and incorporating a stiffness constraint. This optimization approach is eff

Pavement crack and pothole identification are important tasks in transportation maintenance and road safety. This study offers a novel technique for automatic asphalt pavement crack and pothole detection which is based on image processing. Different types of cracks (transverse, longitudinal, alligator-type, and potholes) can be identified with such techniques. The goal of this research is to evaluate road surface damage by extracting cracks and potholes, categorizing them from images and videos, and comparing the manual and the automated methods. The proposed method was tested on 50 images. The results obtained from image processing showed that the proposed method can detect cracks and potholes and identify their severity levels wit