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Menentukan Rute Kendaran Pengangkut Sampah Kota Yogyakarta dengan Algoritma Cheapest Insertion Heuristic Modifikasi Route Construction Hanifah Hanifah; Dian Eka Wijayanti; Aris Thobirin; Puguh Wahyu Prasetyo
Jurnal Fourier Vol. 9 No. 2 (2020)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

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Penelitian ini bertujuan untuk menemukan rute perjalanan kendaraan pengangkut sampah di Kota Yogyakarta. Manfaat penelitian ini yaitu sebagai bahan evaluasi serta pertimbangan dalam pemilihan rute alternatif pengangkutan sampah Kota Yogyakarta. Menggunakan metode dengan perpaduan ilmu matematika secara teori, logika pemikiran, dan ilmu komputasi dengan mengambil lokasi penelitian di Sektor Gunung Ketur yang merupakan bagian dari tanggung jawab Dinas Lingkungan Hidup Kota Yogyakarta. Teori yang digunakan yaitu penggunaan graf berupa graf berbobot dan berarah. Sedangkan algoritma yang digunakan yaitu Cheapest Insertion Heuristic (CIH) yang merupakan bagian dari algoritma Insertion dengan modifikasi Route Construction (RC) yang merupakan salah satu dari metode algoritma Artificial Immune System (AIS). Dengan demikian, penerapan ilmu matematika secara teori dan diperkuat komputasi dapat diterapkan secara nyata. Permasalahan penentuan jalur tercepat maupun efektivitas suatu perjalanan sebenarnya tidak memiliki suatu solusi yang pasti. Tentunya setiap metode memiliki pendekatan masing-masing. Namun, yang perlu diperhatikan adalah kepastian langkah yang digunakan agar langkah tersebut dapat menghasilkan output yang sama meskipun menggunakan metode pendekatan yang berbeda. Hasil yang diperoleh pun sebenarnya tidak sepenuhnya sempurna tetapi hanya menghasilkan beberapa solusi ataupun pilihan yang dapat dijadikan bahan pertimbangan untuk menyelesaikan suatu permasalahan. [This research aims to find the route of the garbage truck in Yogyakarta City. The benefit of this research is to produce the evaluation and the consideration of the selection of alternative routes for transporting the waste in Yogyakarta City. The research has been done by combining theoretical mathematical science, logic, and computational science by focusing on solving the problem at Gunung Ketur Sector, which is under the Environmental Agency of Yogyakarta City. The research used the theory of weighted and directed graphs. Furthermore, the researchers used the Cheapest Insertion Heuristic (CIH), which is a part of the Insertion algorithm with a modified Route Construction (RC), which is one of the methods of Artificial Immune System (AIS) algorithm. Therefore, the application of theoretical mathematical science and computationally could be applied in a real problem. Indeed, the determination of the fastest and the most effective routes has no concrete solutions. Each method has its own approach. However, it is crucial to consider the certainty of the procedure used to produce the same output even though using different ways. The result obtained is not entirely perfect, but the research outcome has made some solutions or alternatives as considerations to solve a problem.]

Kekuatan tak beraturan sisi total pada graf hasil gabungan graf lintasan dengan beberapa kelas graf Setyo Dwi Pratama; Dian Eka Wijayanti
Jurnal Ilmiah Matematika Vol 7, No 1 (2020)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26555/konvergensi.v7i1.19196

Penelitian ini bertujuan untuk menentukan nilai kekuatan tak beraturan sisi total pada graf hasil gabungan graf lingkaran dengan graf lintasan dan graf hasil gabungan dua graf lingkaran masing-masing untuk n sama dengan 3. Pelabelan tak beraturan sisi total pada graf, dengan himpunan titik tak kosong V dan himpunan sisi E suatu fungsi, sehingga bobot setiap sisinya berbeda. Nilai k terkecil pada pelabelan tak beraturan sisi total disebut kekuatan tak beraturan sisi total dari G yang dinotasikan dengan tes G. Selanjutnya, bobot sebuah sisi uv dengan fungsi pelabelan. Berdasarkan pembahasan, dapat disimpulkan bahwa nilai kekuatan tak beraturan sisi total pada graf hasil gabungan graf lingkaran dengan graf lintasan dan graf hasil gabungan dua graf lingkaran yang berturut-turut mempunyai nilai n sama dengan 3.

PELABELAN ANTI AJAIB JARAK PADA SUATU GRAF PETERSEN DIPERUMUM dian eka wijayanti; Aris Thobirin
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 12 No 1 (2020): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2020.12.1.2457

Salah satu jenis pelabelan pada graf adalah pelabelan jarak yang merupakan pelabelan graf berdasarkan jarak antara titik-titiknya. Pelabelan jarak ini disebut distance magic labeling (pelabelan ajaib jarak) jika setiap titik mempunyai bobot pelabelan jarak yang sama. Pelabelan jarak ini disebut distance antimagic labeling (pelabelan anti ajaib jarak) jika setiap titik mempunyai bobot pelabelan jarak yang berbeda. Yang membentuk suatu deret. Tulisan ini membahas tentang pelabelan anti ajaib jarak pada graf petersen diperumum yaitu G= P(n, m) dengan n ≥ 3, 1 ≤ m <n/2 suatu graf teratur berderajat 3 yang mempunyai 2n titik dan 3n sisi. Lebih lanjut, tulisan ini juga membahas tentang pelabelan (a,d)-anti ajaib jarak -{1} pada suatu graf petersen diperumum.

BEBERAPA MODIFIKASI PADA ALGORITMA KRIPTOGRAFI AFFINE CIPHER Dian Eka Wijayanti
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 2 (2018)
Publisher : Diponegoro University

Affine Cipher Cryptography Technique is one of the techniques in classical cryptography which is quite simple so it is very vulnerable to cryptanalysis. Affine cipher's advantage is having an algorithm that can be modified with various techniques. The modifications that can be made to Affine Cipher is to combine Affine cipher's algorithm with other ciphers, replace Affine cipher's key with various functions and matrices and expand the space for plaintext and ciphertexts on Affine cipher. Affine cipher can also be applied to the stream cipher as a keystream generator. This research discusses several modifications of Affine cipher algorithm and performs several other modifications. These modifications are combining Affine Chiper and Vigenere Cipher on , combining Affine, Vigenere and Hill Cipher with invertible matrix applications on . Furthermore, a comparison of the three modifications will be carried out to obtain a new cryptographic method that is more resilient to the cryptanalysis process.

Keamanan Pesan Menggunakan Kriptografi dan Steganografi Least Significant Bit pada File Citra Digital Dian Eka Wijayanti; Wulansari Romadlon
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 10 Issue 2 December 2022
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v10i2.16646

In the current era, data security disturbances often occur, such as data theft by unwanted people. To overcome security problems can be handled using cryptography and steganography methods. The cryptography process generates random writing that can obscure the message making it difficult for others to read. However, cryptography itself is still too weak to secure messages, so steganography is needed to disguise the existence of the message so that it is not visible to the human eye. Apart from hiding messages, another goal is to know the impact of message insertion. In this study, the encryption steps were followed by insertion and decryption followed by extraction. In the secret message encryption process using two algorithms, namely Vigenere Cipher and Playfair Cipher. In the process of inserting a secret message using Least Significant Bit (LSB) steganography. The results of the combination of cryptography and steganography are able to secure secret messages without causing significant changes even though the digital image used before and after the steganography process has increased in size, the Mean Square Error (MSE) value obtained is 0.000136 and the Peak Signal to Noise Ratio (PSNR) value is obtained. 86.8062 dB and the result of message encryption is enough to obscure the relationship pattern in the modified secret message with an avalanche effect value of 53.06%.

Pelabelan Jarak Tak Teratur Titik Pada Graf Persahabatan Lengkap Diperumum Cindy Ainun Majid; Dian Eka Wijayanti; Aris Thobirin; Puguh Wahyu Prasetyo
Limits: Journal of Mathematics and Its Applications Vol 20, No 1 (2023)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v20i1.7917

Graph labeling is the labeling of graph elements such as vertex, edge and both. distance vertex irregular labeling is a type of labeling resulting from the development of distance magic labeling and (a, b)-distance anti-magic labeling. Let , be a simple graph. The distance vertex irregular labeling of is a vertex labeling so that the weight of each vertex is different. The weight of is calculated based on the sum of vertices label in the set of neighboring vertex , namely Distance vertex irregularity strength of , denoted as d , is the smallest value of the largest label so that has a distance vertex irregular labeling. This study aims to construct a generalized complete friendship graph , determine the labeling function, determine the distance vertex irregularity strength then formulate and prove the theorem resulting from the labeling. The object of this research is to label each vertex on a generalized complete friendship graph. This research method is a literature study obtained through various sources. Based on the research results, it is known that the graph has distance vertex irregular labeling. For an integer m and n, , the labeling function of is and . Distance vertex irregularity strength of generalized complete friendship graph is .

Total distance vertex irregularity strength of some corona product graphs Dian Eka Wijayanti; Noor Hidayat; Diari Indriati; Abdul Rouf Alghofari; Slamin Slamin
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.1.17

A distance vertex irregular total k-labeling of a simple undirected graph G = G(V, E), is a function f : V(G)∪E(G)→{1, 2, …, k} such that for every pair vertices u, v ∈ V(G) and u ≠ v, the weights of u and v are distinct. The weight of vertex v ∈ V(G) is defined to be the sum of the label of vertices in neighborhood of v and the label of all incident edges to v. The total distance vertex irregularity strength of G (denoted by tdis(G)) is the minimum of k for which G has a distance vertex irregular total k-labeling. In this paper, we present several results of the total distance vertex irregularity strength of some corona product graphs.

On Distance Vertex Irregular Total k-Labeling Dian Eka Wijayanti; Noor Hidayat; Diari Indriati; Abdul Rouf Alghofari; Slamin
Science and Technology Indonesia Vol. 8 No. 3 (2023): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2023.8.3.479-485

Let H= (T,S), be a finite simple graph, T(H)= T and S(H)= S, respectively, are the sets of vertices and edges on H. Let σ:T∪S→1,2,· · · ,k, be a total k-labeling on H and wσ(x), be a weight of x∈T while using σ labeling, which is evaluated based on the total number of all vertices labels in the neighborhood x and its incident edges. If every x∈T has a different weight, then σ is a distance vertex irregular total k-labeling (DVITL). Total distance vertex irregularity strength of H (tdis(H) is defined as the least k for which H has a DVITL. Our research investigates the DVITL of the path (Pr) and cycle (Cr) graphs. We establish a lower bound and then calculate the precise value of tdis(Pr) and tdis(Cr).

PELABELAN ANTI AJAIB JARAK PADA SUATU GRAF PETERSEN DIPERUMUM dian eka wijayanti; Aris Thobirin
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Vol 12 No 1 (2020): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2020.12.1.2457

Salah satu jenis pelabelan pada graf adalah pelabelan jarak yang merupakan pelabelan graf berdasarkan jarak antara titik-titiknya. Pelabelan jarak ini disebut distance magic labeling (pelabelan ajaib jarak) jika setiap titik mempunyai bobot pelabelan jarak yang sama. Pelabelan jarak ini disebut distance antimagic labeling (pelabelan anti ajaib jarak) jika setiap titik mempunyai bobot pelabelan jarak yang berbeda. Yang membentuk suatu deret. Tulisan ini membahas tentang pelabelan anti ajaib jarak pada graf petersen diperumum yaitu G= P(n, m) dengan n ≥ 3, 1 ≤ m <n/2 suatu graf teratur berderajat 3 yang mempunyai 2n titik dan 3n sisi. Lebih lanjut, tulisan ini juga membahas tentang pelabelan (a,d)-anti ajaib jarak -{1} pada suatu graf petersen diperumum.

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