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All Journal Jurnal Edukasi Universitas Jember KADIKMA CAUCHY: Jurnal Matematika Murni dan Aplikasi Tadris: Jurnal keguruan dan Ilmu Tarbiyah JINOP (Jurnal Inovasi Pembelajaran) UNEJ e-Proceeding BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Indiktika : Jurnal Inovasi Pendidikan Matematika EDUPEDIA INTEGRITAS : Jurnal Pengabdian JURNAL AXIOMA : Jurnal Matematika dan Pembelajaran JPKMI (Jurnal Pengabdian Kepada Masyarakat Indonesia) Contemporary Mathematics and Applications (ConMathA) Jurnal Pengabdian Masyarakat Khatulistiwa Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika Jurnal Kependidikan: Jurnal Hasil Penelitian dan Kajian Kepustakaan di Bidang Pendidikan, Pengajaran dan Pembelajaran Jurnal Diferensial CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Pancaran Pendidikan Jurnal Pengabdian Masyarakat Bangsa Jurnal Ilmiah Matematika (JIMAT)
Arika Indah Kristiana
Universitas Jember
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b-Chromatic Number of Tree Graph Families Prihandini, Rafiantika Megahnia; Kristiana, Arika Indah; Dana, Lusita Risma; Wihardjo, Edy; Adawiyah, Robiatul; Zulnaidi, Hutkemri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.32328

Abstract

Tree graph is a connected graph and has no circuits. Tree graphs used in this study include: broom graph, firework graph, banana tree graph, centipede graph, E graph, and double star graph. Graph coloring is the process of giving color to graph elements with the rule that neighboring elements must not have the same color and the number of colors used must be as minimal as possible. b-Coloring of a graph G is a coloring of the vertices of G such that each color class has at least one vertex adjacent to all other color classes. The b-Chromatic number of a graph G is denoted by φ (G), is the largest integer k such that G has a b-coloring with k colors. The limit of b-coloring of graph G with maximum degree ∆(G) is as follows. χ(G)≤φ(G)≤∆(G)+1.χ(G) is the chromatic number of a graph G where χ(G) is the minimum value of the color required for proper coloring of graph G. While ∆(G) is the maximum degree of the vertices in graph G. This study uses an exploratory research type with axiomatic deductive method and pattern detection method. Based on the results of this study, the results of the b-coloring analysis on the tree graph family are known. The results of this study are expected to be used as study material and development of scientific knowledge related to b-coloring of other graphs
Super (a, d)-hyperedge antimagic total labeling on hypergraphs of the volcano graph, semi parachute graph, and comb product graph Adawiyah, Robiatul; Asari, Okta Endri; Dafik, Dafik; Kristiana, Arika Indah; Prihandini, Rafiantika Megahnia; Rohini, A
Alifmatika (Jurnal pendidikan dan pembelajaran Matematika) Vol 7 No 2 (2025): Alifmatika - December
Publisher : Fakultas Tarbiyah Universitas Ibrahimy

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35316/alifmatika.2025.v7i2.391-408

Abstract

In graph theory, understanding the labeling of graphs and hypergraphs provides valuable insights into their structural properties and applications. A hypergraph generalizes the notion of a conventional graph, defined as a mathematical structure built from a vertex set V and a hyperedge set E, where each hyperedge is allowed to connect two or more vertices simultaneously. The essential distinction between a graph and a hypergraph lies in their edges. While in a graph a single edge connects exactly two vertices, in a hypergraph a single hyperedge may connect any number of vertices, including two. A hypergraph is considered to admit a super (a, d) -hyperedge antimagic total labeling, such that the vertex label functions f: V(H)  1, 2, 3, ....., V(H) then f: E(H)  V(H) + 1, ....., V(H) + V(H) and weight w(ei) = ∑ f(ei) + ∑ f(Vi,j), where i denotes the number of hyperedges, j represents the number of vertices contained in a hyperedge, and e_i refers to the set of vertices and its associated edges with weight w(ei) for each hyperedge. A super (a, d) -hyperedge antimagic total labeling is formulated as a labeling scheme based on arithmetic progressions, where ???? serves as the initial value and d denotes the common difference between consecutive labels. In this scheme, the total weight of a hyperedge is determined by deriving from the sum of the vertex labels and the label of the respective hyperedge. The labels are arranged in an arithmetic sequence, ensuring that each hyperedge has a distinct weight. This study focuses on several special classes of hypergraphs, namely, the volcano graph, the semi-parachute graph, and the comb product of graphs, to implement and examine the characteristics of the super (a, d)-hyperedge antimagic total labeling. By focusing on these graph classes, the study contributes to combinatorics by offering a deeper understanding of hypergraph labeling schemes and their potential applications in network theory, coding theory, and data modeling.
Application on Hypergraph in Vigenere Chiper Asari, Okta Endri; Dafik, Dafik; Adawiyah, Robiatul; Kristiana, Arika Indah; Prihandini, Rafiantika Megahnia
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34572

Abstract

Message protection remains a major focus in the field of cryptography. This study proposes a new development on the Caesar cipher algorithm by utilizing hypergraph as a keystream generation source. The research designs a super (a,d)-hyperedge antimagic total labeling method applied to three hypergraph structures (Volcano, Semi Parachute, and Comb) to generate the keystream. Security is evaluated using four mechanisms: brute force analysis, processing time, ciphertext character distribution, and ciphertext bit size. The findings prove that the hypergraph based approach is robust against brute force attacks, improve memory and time efficiency. Quantitatively, the Comb hypergraph demonstrates the best efficiency, achieving an encryption time of 0.0030 seconds for 512 bytes and superior storage efficiency (e.g., 136 bytes for 16 bytes ), outperforming the Semi Parachute and Volcano structures. The main contributions include the hypergraph labeling-based keystream generation algorithm, dynamic block key construction, and a Vigenere protocol that is more adaptive to storage constraints and computationally efficient..
Co-Authors Afni, Anis Nur Agatha, Alvian Bagus Ahmad Aji Aima, Muslihatul Aji, Ahmad Arif Fatahillah Arifandi, Agus Asari, Okta Endri Asy’ari, Muhammad Lutfi Aziza, Adinda Putri Azizah, Zakiyah Lina Nur A’yun, Qurrotul Bunga Ayu Desy Permatasari, Bunga Ayu Cahyadewi, Karina Cindy Cici Fitri Lestari, Cici Fitri D Dimas, D D. Dafik Dafik Dana, Lusita Risma Deddy Setiawan Deddy Setiawan Deddy Setyawan Desi Febriani Putri Devira Ayu Nurandari, Devira Ayu Dewi Santi, Dewi Dewi, Ernita Sukarno Dian Kurniati Didik Sugeng Pambudi Dimas Ardiansyah Ramadhan Dinar Dwi Yuliyanti Dinawati Trapsilasiwi Dliou, Kamal Dwi Agustin Retnowardani Dwi Roby Pramono Dwi Sylvia Hanafi Edy Wihardjo Eka Cahya Lestari, Eka Cahya Eka Wulandari Fauziah, Eka Wulandari Eko Gunariyanto Elsa Yuli Kurniawati Ema Desia Prajitiasari Erica Dian P Ermita Rizki Albirri Ernita Sukarno Dewi, Ernita Fatimah, Laila Nurul Fihrisi, Fathan Hobri I Made Tirta I Made Tirta Intan Nurul Awwaliyah Islamiah, Maulidi Arsih Umaroh Ja'far, Muhammad Jatmiko, Dhanar Dwi Hary Karina Cindy Cahyadewi Karuniaji Fitra Insani Khilyah Munawaroh Khusnul, Agustina Hotimatus Kurniawati, Elsa Yuli Kusbudiono Kusbudiono, Kusbudiono Kusumawati, Nurita Lestari, Deninta Dwi Ayu Lestari, Nurcholif Diah Sri Lioni Anka Monalisa, Lioni Anka Marmono Singgih Miftahul Jannah Mohammad Fadli Rahman Muhammad Gufronil Halim Muhammad Lutfi Asy’ari Muhammad Usaid Hudloir Murtini Murtini, Murtini Niswatul Imsiyah Nur Safrida, Lela Nurbuono, Mousthapaa Nurcholif Diah Sri Lestari Nurina Anggun Ratnaningtyas Nuroeni, Ilmiatun Osman, Sharifah Prahastiwi, Lusi Rizzami Pratiwi, Alfiani Dyah Prihandini, Rafiantika M. Prihandini, Rafiantika Megahniah Pujiyanto, Arif Putra, Aldi Maulana Qurrotul A’yun Rafelita Faradila Sandi Rafiantika Megahnia Prihandini Rahmawati, Mira Randi Pratama Murtikusuma Ratna Dwi Christyanti, Ratna Dwi Retno Nur Khasanah Ridho Alfarisi Ridho Alfarisi, Ridho Ridlo, Zainur Rasyid Rizky Astarina, Rizky Robiatul Adawiyah Robiatul Adawiyah Rohini, A S Suharto S Sunardi S Susanto Saddam Hussen Santoso, Aji Mansur Saputra, Guntari Setiawan, Renal Heldi Siddiqui, M. Kamran Siti Aisyah Slamin Sumani . Surya Indriani Susanto Susanto Susanto, Arnis Budi Susi Setiawani Syahputri, Vika Thoyibah, Fifi Tika Nurpitasari Titik Sugiarti Titin Kartini Toto Bara Setiawan Umi Azizah Anwar WIHARDJO, EDY Wirdah Pramita N Yanuarsih, Elly Zainur Rasyid Ridlo Zulnaidi, Hutkemri