. Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper,we introduce the generalized Cayley graph denoted by  which is a graph with a vertex set consisting of all column matrices  in which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of the similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and  and m . We aim to provide some basic properties of the new graph and determine the structure of  when  is a complete graph  for every , and n, m  .

      In this Ë‘work, we present theË‘ notion of the Ë‘graph for a KU-semigroup  as theË‘undirected simple graphË‘ with the vertices are the elementsË‘ of  and weË‘Ë‘study the Ë‘graph ofË‘ equivalence classesË‘ofË‘  which is determinedË‘ by theË‘ definition equivalenceË‘ relation ofË‘ these verticesË‘, andË‘ then some related Ë‘properties areË‘ given. Several examples are presented and some theorems are proved. ByË‘ usingË‘ the definitionË‘ ofË‘ isomorphicË‘ graph, Ë‘we showË‘ thatË‘ the graphË‘ of equivalence Ë‘classes Ë‘and the Ë‘graphË‘of Ë‘a KU-semigroup Ë‘  areË‘ theË‘ sameË‘,

Let A ⊆ V(H) of any graph H, every node w of H be labeled using a set of numbers; , where d(w,v) denotes the distance between node w and the node v in H, known as its open A-distance pattern. A graph H is known as the open distance-pattern uniform (odpu)-graph, if there is a nonempty subset A ⊆V(H) together with  is the same for all . Here  is known as the open distance pattern uniform (odpu-) labeling of the graph H and A is known as an odpu-set of H. The minimum cardinality of vertices in any odpu-set of H, if it exists, will be known as the odpu-number of the graph H. This article gives a characterization of maximal outerplanar-odpu graphs. Also, it establishes that the possible odpu-number of an odpu-maximal outerplanar graph i

Most of the Internet of Things (IoT), cell phones, and Radio Frequency Identification (RFID) applications need high speed in the execution and processing of data. this is done by reducing, system energy consumption, latency, throughput, and processing time. Thus, it will affect against security of such devices and may be attacked by malicious programs. Lightweight cryptographic algorithms are one of the most ideal methods Securing these IoT applications. Cryptography obfuscates and removes the ability to capture all key information patterns ensures that all data transfers occur Safe, accurate, verified, legal and undeniable.  Fortunately, various lightweight encryption algorithms could be used to increase defense against various at

Worldwide, enormous amounts of waste cause major environmental issues, including scrap tires and plastic, and large waste, a consequence of the demolition of buildings, including crushed concrete, crushed clay bricks, and crushed thermo-stone. From that point, it’s possible to consider that the recycling processes for these materials and using them in the manufacturing field will reduce the adverse effects on the environment of these wastes and the consumption of natural resources. Sustainable concrete blocks can be considered as one of the products produced by using these materials as partial volume replacement of the coarse, fine aggregate, or cement content, considering their dry density, workability, absorption, co

          A total global dominator coloring of a graph  is a proper vertex coloring of  with respect to which every vertex  in  dominates a color class, not containing  and does not dominate another color class. The minimum number of colors required in such a coloring of  is called the total global dominator chromatic number, denoted by . In this paper, the total global dominator chromatic number of trees and unicyclic graphs are explored.

The aim of this paper is to introduce and study a new kind of graphs associated to an ideal of a commutative ring. Let â„› be a commutative ring with identity, and I(â„›) be the set of all non-trivial ideals of â„› with S I(â„›). The sum ideal graph associated to S, denoted by       Î¨(â„›, S), is the undirected graph with vertex set {A I(â„›): S⊂A+B, for some B I(â„›)} where two ideal vertices A and B are adjacent if and only if A B and S⊂A+B. In this paper we establish some of characterizations and results of this kind of graph with providing some examples.

Fractal image compression depends on representing an image using affine transformations. The main concern for researches in the discipline of fractal image compression (FIC) algorithm is to decrease encoding time needed to compress image data. The basic technique is that each portion of the image is similar to other portions of the same image. In this process, there are many models that were developed. The presence of fractals was initially noticed and handled using Iterated Function System (IFS); that is used for encoding images. In this paper, a review of fractal image compression is discussed with its variants along with other techniques. A summarized review of contributions is achieved to determine the fulfillment of fractal image co

     Block cipher technique is one of cryptography techniques to encrypt data block by block. The Serpent is one of AES candidates. It encrypts a 128-bit block by using 32 rounds of a similar calculation utilizing permutations and substitutions. Since the permutations and substitutions of it are static. Then this paper proposes dynamic methods for permutation, substitution and key generation based on chaotic maps to get more security. The proposed methods are analyzed and the results showed that they were able to exceed the weakness resulting from the use of static permutations and substitutions boxes in the original algorithm and also can reduce number of rounds and time usage compared with a classical Serpent block