Abstract. Let G be a simple graph of order p and size q.G r a p hG is called an (a, d)-edge-antimagic total if there exist a bijection f : V (G) ∪ E(G) →{1, 2,...,p+ q} such that the edge-weights, w(uv)= f (u)+f (v)+f (uv); u, v ∈ V (G),uv ∈ E(G),formanarithmeticsequencewithfirstterma and common difference d.S u c hag r a p hG is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge antimagic total properties of connected of Ferris Wheel FWm,n by using deductive axiomatic method. The results of this research are a lemma or theorem. The new theorems show that a connected ferris wheel graphs admit a super (a, d)-edge antimagic total labeling for d =0, 1, 2.I tc a nb ec o n c l u d e dt h a tt h er e s u l to ft h i sr e s e a r c hh a sc o v e red all feasible d.

The condition of the world experiencing the COVID-19 pandemic has resulted in some daily activities limited by health protocols. The Indonesian government's policy in the academic field has forced STIE Mandala Jember, as one of the private universities, to implement online-based new student admissions. The registrant's identity must be kept confidential during the online-based new student registration process, so the running system needs an identity coding (encryption) process. Hill Cipher is a cryptographic algorithm that utilizes the multiplication of matrix inverse operations. In ordinary Hill Cipher, to encrypt the entire plaintext, a key is needed. In this paper, we will modify the Hill Cipher named Hill Cipher Chain. The process of chained Hill Cipher will encrypt and decrypt the primary key based on the previous character. Firstly, we will encrypt the primary key with the key from the next column of the database. In this case, we use the name column. The encryption result will be used as a key for the subsequent character encryption. Implementation of this method makes the difficulty level of decryption more complex than the ordinary Hill Cipher, which only uses one key for all so that the security of the data obtained is also getting better.

We propose a new steganography method to hide an image into another image using matrix multiplication operations on max-plus algebra. This is especially interesting because the matrix used in encoding or information disguises generally has an inverse, whereas matrix multiplication operations in max-plus algebra do not have an inverse. The advantages of this method are the size of the image that can be hidden into the cover image, larger than the previous method. The proposed method has been tested on many secret images, and the results are satisfactory which have a high level of strength and a high level of security and can be used in various operating systems.

Non-linear equations system is a collection of some non-linear equations that will find the best solution. Finding the solution of non-linear equations system usually by using analytical method, but there are some complex cases that cannot be solved analytically, so new methods are needed to solve them. One method that can be used to solve non-linear equations system is by using metaheuristic algorithm. This research aims to solve non-linear equations system with complex roots by using metaheuristic algorithm. The metaheuristic algorithm used in this research is Particle Swarm Optimization (PSO), Firefly Algorithm (FA) and Cuckoo Search (CS). The input of this research is non-linear equations system that will be tested and parameters of the PSO, FA, and CS algorithm. Non-linear equations system which is the object of problem is polynomial function and transcendent function, which include logarithmic function, first degree trigonometric function and exponential function. The resulting output is an approximation of the complex roots and function value. Then the obtained solution of non-linear equations system compared with the result of accuracy by finding the value of the function f(x) which is closer to zero. The result of this research obtained by comparing the value of the function produced by each algorithm showed that Particle Swarm Optimization (PSO) algorithm is better at solving non-linear equations system with complex roots because the value of the resulting function is close to zero.

As science developed, heuristic methods began to be used in graph coloring. Heuristic methods that have been used for graph coloring include Genetic Algorithm, Tabu Search, and Ant Colony Algorithm. A Genetic Algorithm is a method for solving optimization problems. In this study, the Genetic Algorithm will be used for the issue of labeling irregular vertices of inclusive distances to label any graph inclusively. We restrict an inclusive 1-distance to a simple graph using one-point crossover and mutation. The steps are a generation of random chromosomes, evaluating chromosome fitness values with tournament selection, conducting an evolutionary process consisting of one-point crossover and mutation, repeating the process until the termination criteria are met. The results of implementing the genetic algorithm on inclusive labeling can be determined by the chromatic number based on the adjacency matrix. The results of this labeling can be used as an alternative solution to the problem of inclusive labeling.Keywords: Genetic Algorithm; graph labeling; inclusive labeling. AbstrakSeiring berkembangnya ilmu pengetahuan metode heuristic mulai digunakan dalam pewarnaan graf. Metode heuristic yang telah digunakan untuk pewarnaan graf antara lain Algoritma Genetika, Tabu Search, dan Algoritma Semut (Ant Colony). Algoritma Genetika merupakan metode untuk menyelesaikan masalah optimasi. Pada penelitian ini, Algoritma Genetika digunakan untuk masalah pelabelan titik tak-teratur jarak inclusive agar dapat melabeli sebarang graf secara inclusive. Kami membatasi lingkup penelitian dengan menerapkan jarak inclusive 1 pada graf sederhana, menggunakan crossover satu titik dan mutasi. Metode yang digunakan dalam penelitian ini adalah studi literatur dengan mengkaji penggunaan Algoritma Genetika pada pelabelan titik tak-teratur jarak inclusive suatu graf. Langkah-langkah yang dilakukan adalah: pembangkitan kromosom secara acak, evaluasi nilai fitness kromosom dengan tournament selection, melakukan proses evolusi yang terdiri dari crossover satu titik dan mutasi, perulangan proses sampai kriteria pemerhentian terpenuhi. Hasil implementasi algoritma genetika pada pelabelan inclusive adalah dapat mengetahui bilangan kromatik berdasarkan matriks adjacency. Hasil pelabelan ini dapat dijadikan sebagai salah satu alternatif penyelesaian masalah pelabelan inklusif. Kata Kunci : Algoritma Genetika; pelabelan graf; pelabelan inklusif.