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All Journal IJCCS (Indonesian Journal of Computing and Cybernetics Systems) Ilmu Pendidikan BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Manajemen Informatika Jurnal Karinov InPrime: Indonesian Journal Of Pure And Applied Mathematics Jurnal Pembelajaran, Bimbingan, dan Pengelolaan Pendidikan Jurnal MIPA dan Pembelajarannya Journal of Innovation and Teacher Professionalism Jurnal ilmiah teknologi informasi Asia
Mahmuddin Yunus
Universitas Negeri Malang
Arts Humanities Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Immunology & microbiology Languange, Linguistic, Communication & Media Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Rainbow Connection Number of Octopus Iteration Graphs Rahmadani, Desi; Giyanatta, Adinda Evelyn; Pratiwi, Dina; Yunus, Mahmuddin; Kusumasari, Vita
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 6, No 2 (2024)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v6i2.41414

Abstract

The rainbow connection number of a graph G denoted by rc(G) is the minimum number of colors used to color the edges in G, such that every pair of vertices is connected by a path with all different colors. In 2008, Chartrand et al. first introduced the concept of rainbow connection numbers. They introduced it as an edge coloring on a graph that refers to the path of each pair of vertices. An octopus graph, with m legs denoted by Om, is a graph constructed from a fan graph Fm and a star graph Sm. The graphs studied in this article are two classes of octopus iteration graphs, namely the octopus chain graph and the octopus ladder graph. The octopus chain graph, denoted by O2(n) is a graph constructed from n copies of O2 and connecting one leg of the i-th copy to the (i+1)-th copy, for every I = 1,2,..., n-1. The octopus ladder graph, denoted by O2'(n) is a graph constructed from graph O2(n) by connecting one of vertex of degree two of the i-th copy to the (i+1)-th copy. In this research, we determine the rainbow connection number of the octopus chain graphs O2(n) and the octopus ladder graphs O2'(n). We obtain that rc(O2(n))=3n, for n >= 1 and rc(O2'(n))=3n-1,  for n >= 2.Keywords: Classes of octopus iteration graphs; Octopus chain graph; Octopus ladder graph; Rainbow connection number. AbstrakBilangan terhubung pelangi pada graf G dinotasikan dengan rc(G)  merupakan jumlah warna minimum yang digunakan untuk mewarnai sisi pada G, sehingga setiap pasang titik dihubungkan oleh suatu lintasan dengan warna yang berbeda semua. Pada tahun 2008, Chartrand dkk. pertama kali memperkenalkan konsep bilangan terhubung pelangi. Chartrand dkk. memperkenalkannya sebagai pewarnaan sisi pada graf yang mengacu pada lintasan setiap pasang titiknya. Graf gurita dengan m kaki dinotasikan denganOm  adalah graf yang dikonstruksi dari graf kipas Fm  dan graf bintang Sm. Graf yang dikaji dalam artikel ini merupakan dua kelas graf iterasi gurita, yaitu graf rantai gurita dan graf tangga gurita. Graf rantai gurita yang dinotasikan dengan O2(n) adalah graf yang dikonstruksi dari n copy graf Om dan menghubungkan satu kaki salinan ke-i ke salinan ke-i+1, untuk setiap i = 1,2,...,n. Graf tangga gurita yang dinotasikan dengan O2'(n)  adalah graf yang dibangun dari graf O2(n) dengan menghubungkan salah satu titik berderajat dua salinan dari graph ke-i ke salinan ke-i+1. Pada penelitian ini, ditentukan bilangan terhubung pelangi pada graf rantai gurita O2(n) dan graf tangga gurita O2'(n). Kami memperoleh bahwa rc(O2(n))=3n untuk n>=1 dan rc(O2'(n))=3n-1, untuk n>=2. Kata Kunci: Kelas graf iterasi gurita; Graf rantai gurita; Graf tangga gurita; Bilangan terhubung pelangi. 2020MSC: 05C15, 05C40.
PRIME LABELING OF AMALGAMATION OF FLOWER GRAPHS Rahmadani, Desi; Aldiansyah, Ardi; Pratiwi, Dina; Yunus, Mahmuddin; Kusumasari, Vita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2431-2442

Abstract

Graph labeling is the assigning of labels represented by integers or symbols to graph elements, edges and/or vertices (or both) of a graph. Consider a simple graph with a vertex-set and an edge-set . The order of graph , denoted by , is the number of vertices on . The prime labeling is a bijective function , such that the labels of any two adjacent vertices in G are relatively prime or , for every two adjacent vertices and in . If a graph can be labeled with prime labeling, then the graph can be said to be a prime graph. A flower graph is a graph formed by helm graph by connecting its pendant vertices (the vertices have degree one) to the central vertex of , such a flower graph is denoted as In this research, we employ constructive and analytical methods to investigate prime labelings on specific graph classes. Definitions, lemmas, and theorems are developed as the main results in this research. The amalgamation is a graph formed by taking all by taking all the and identifying their fixed vertices . If , then we write with . In previous research, it has been shown that the flower graphs , for are prime graphs. Continuing the research, we prove that two classes of amalgamation of flower graphs are prime graphs.
PERANAN MULTIMEDIA KOMPUTER DALAM MENINGKATKAN PROSES BELAJAR MENGAJAR Yunus, Mahmuddin
Jurnal Ilmiah Teknologi Informasi Asia Vol 2 No 1 (2007): Volume 2 Nomor 1 (5)
Publisher : LP2M Institut Teknologi dan Bisnis ASIA Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

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Rainbow Connection Number of Octopus Iteration Graphs Rahmadani, Desi; Giyanatta, Adinda Evelyn; Pratiwi, Dina; Yunus, Mahmuddin; Kusumasari, Vita
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 6 No. 2 (2024)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v6i2.41414

Abstract

The rainbow connection number of a graph G denoted by rc(G) is the minimum number of colors used to color the edges in G, such that every pair of vertices is connected by a path with all different colors. In 2008, Chartrand et al. first introduced the concept of rainbow connection numbers. They introduced it as an edge coloring on a graph that refers to the path of each pair of vertices. An octopus graph, with m legs denoted by Om, is a graph constructed from a fan graph Fm and a star graph Sm. The graphs studied in this article are two classes of octopus iteration graphs, namely the octopus chain graph and the octopus ladder graph. The octopus chain graph, denoted by O2(n) is a graph constructed from n copies of O2 and connecting one leg of the i-th copy to the (i+1)-th copy, for every I = 1,2,..., n-1. The octopus ladder graph, denoted by O2'(n) is a graph constructed from graph O2(n) by connecting one of vertex of degree two of the i-th copy to the (i+1)-th copy. In this research, we determine the rainbow connection number of the octopus chain graphs O2(n) and the octopus ladder graphs O2'(n). We obtain that rc(O2(n))=3n, for n >= 1 and rc(O2'(n))=3n-1,  for n >= 2.Keywords: classes of octopus iteration graphs; octopus chain graph; octopus ladder graph; rainbow connection number. AbstrakBilangan terhubung pelangi pada graf G dinotasikan dengan rc(G)  merupakan jumlah warna minimum yang digunakan untuk mewarnai sisi pada G, sehingga setiap pasang titik dihubungkan oleh suatu lintasan dengan warna yang berbeda semua. Pada tahun 2008, Chartrand dkk. pertama kali memperkenalkan konsep bilangan terhubung pelangi. Chartrand dkk. memperkenalkannya sebagai pewarnaan sisi pada graf yang mengacu pada lintasan setiap pasang titiknya. Graf gurita dengan m kaki dinotasikan denganOm  adalah graf yang dikonstruksi dari graf kipas Fm  dan graf bintang Sm. Graf yang dikaji dalam artikel ini merupakan dua kelas graf iterasi gurita, yaitu graf rantai gurita dan graf tangga gurita. Graf rantai gurita yang dinotasikan dengan O2(n) adalah graf yang dikonstruksi dari n copy graf Om dan menghubungkan satu kaki salinan ke-i ke salinan ke-i+1, untuk setiap i = 1,2,...,n. Graf tangga gurita yang dinotasikan dengan O2'(n)  adalah graf yang dibangun dari graf O2(n) dengan menghubungkan salah satu titik berderajat dua salinan dari graph ke-i ke salinan ke-i+1. Pada penelitian ini, ditentukan bilangan terhubung pelangi pada graf rantai gurita O2(n) dan graf tangga gurita O2'(n). Kami memperoleh bahwa rc(O2(n))=3n untuk n>=1 dan rc(O2'(n))=3n-1, untuk n>=2. Kata Kunci: kelas graf iterasi gurita; graf rantai gurita; graf tangga gurita; bilangan terhubung pelangi. 2020MSC: 05C15, 05C40.
Co-Authors Agus Harjoko Aldiansyah, Ardi Ansyari, Huda Denis Eka Cahyani Desi Rahmadani Dina Pratiwi, Dina Giyanatta, Adinda Evelyn Irsyad, Luluk Nur Hidayati Lucky Tri O Mardikasari, Finda Mimiep Setyowati Madja Pratiwi, Rachel Theresa Laras Pujiyanto Pujiyanto Rahmadani, Desi Rifki Diva Riyanto Rony, Zahara Tussoleha Sisworo Swalaganata, Galandaru Tarusu, Shinta Aplian Vita Kusumasari