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All Journal Prosiding Seminar Matematika dan Pendidikan Matematik Jurnal Pendidikan (Teori dan Praktik) JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Masyarakat Merdeka (JMM) JIPI (Jurnal Ilmiah Penelitian dan Pembelajaran Informatika) TELKA - Telekomunikasi, Elektronika, Komputasi dan Kontrol Gammath : Jurnal Ilmiah Program Studi Pendidikan Matematika Jurnal Pengabdian Masyarakat IPTEKS JUSTINDO (Jurnal Sistem dan Teknologi Informasi Indonesia) Kontribusia : Research Dissemination for Community Development Suluah Bendang: Jurnal Ilmiah Pengabdian Kepada Masyarakat Journal of Mathematics Education and Science BIOS : Jurnal Teknologi Informasi dan Rekayasa Komputer Archive: Jurnal Pengabdian Kepada Masyarakat JP (Jurnal Pendidikan) : Teori dan Praktik International Journal of Trends in Mathematics Education Research (IJTMER) Jurnal Aplikasi Sistem Informasi dan Elektronika Scientific Journal of Informatics Journal of Digital Literacy and Volunteering JUSTINDO (Jurnal Sistem dan Teknologi Informasi Indonesia)
Saifudin, Ilham
Universitas Muhammadiyah Jember
Religion Agriculture, Biological Sciences & Forestry Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Education Electrical & Electronics Engineering Engineering Environmental Science Languange, Linguistic, Communication & Media Mathematics Public Health Social Sciences Other

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Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

 1 
The Four-Distance Domination Number in the Ladder and Star Graphs Amalgamation Result and Applications Ilham Saifudin; Hardian Oktavianto; Lutfi Ali Muharom
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 2 (2022): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i2.6628

Abstract

The study purpose is to determine the four-distance domination number in the amalgamation operation graph, namely the vertex amalgamation result graph of ladder graph Amal(L_m,v,n) with m≥2 and n≥2 and the vertex amalgamation result graph of a star graph with its name Amal(S_m,v,n) with m≥2 and n>2. In addition, the application use the Four-distance domination number on Jember Regency Covid-19 taskforce post-placement. The Importanceof this research, namely the optimal distribution of the Covid-19 task force post. It is not just doing mask surgeries every day on the streets. The optimal referred to can be in the form of integrated handlers in each sub-district or points that are considered to need fast handling so that coordination between posts can respond and immediately identify cases of transmission and potential infections due to interactions with patients who are already positive. The methods used in this research are pattern recognition and axiomatic deductive methods. The results of this study include:γ_4 (Amal(S_m,v,n))=1; for m≥2 and n≥2, γ_4 (Amal(L_m,v,n))={■(1; for 2≤m≤4 @⌊m/8⌋n+1 for m≡0,1,2,3,4 (mod 8)@⌈m/8⌉n; for others m ) ┤ and based on the Indonesia Country, Jember Regency Map, 2 Covid 19 task-force posts are needed to be placed in Balung and Kalisat sub-districts using the Four-distance domination number application. 
Domination Numbers in Graphs Resulting from Shackle Operations with Linkage of any Graph Saifudin, Ilham; Widiyaningtyas, Triyanna; Rhomdani, Rohmad Wahid; Dasuki, Moh.
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.19675

Abstract

The domination number is the number of dominating nodes in a graph that can dominate the surrounding connected nodes with a minimum number of dominating nodes. This domini number is denoted by γ(G). In this research, we will examine the domination number of the distance between two graphs resulting from the shackle operation with any graph as linkage. This differs from previous research, namely the domination of numbers at one and two distances. This study emphasizes how the results of operations on the shackle are connected to the shackle graph as any graph connects the copy. Any graph here means all graphs are connected and generally accepted. The method used in this research is pattern recognition and axiomatic deductive methods. The pattern detection method examines patterns where a graph's number of dominating points can dominate the connected points around it with a minimum number of dominating nodes. Meanwhile, axiomatic deductive is a research method that uses the principles of deductive proof that apply to mathematical logic by using existing axioms or theorems to solve a problem. The Result of graph S_n with t copies and S_m as linkage, then the two-distance domination number in the graph resulting from the shackle operation is γ_2 (Shack(S_n,S_m,t) )=t-1; graph S_n with t copies and C_m as linkage, then the two-distance domination number in the graph resulting from the shackle operation is γ_2 (Shack(S_n,C_m,t) )={■(t,for 3≤m≤6@⌈n/5⌉(t-1),for m≥7)┤; graph C_n with t copies and S_m as linkage, then the two-distance domination number in the graph resulting from the shackle operation isγ_2 (Shack(C_n,S_m,t) )={■(t-1,for n=3@t,for 4≤n≤5@⌈n/5⌉t,for n≥6)┤ This research provides benefits and adds to research results in the field of graph theory specialization of two-distance domination numbers in the result graph of shackle operation with linkage any graph.
Local Partition Dimension of Grid Graph and Its Application to the Coordinates of Potential Disaster Areas in Jember Regency Saifudin, Ilham; Umilasari, Reni; Rizal, Nanang Saiful
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.15798

Abstract

Partition dimension was introduced as a part of interesting topic in graph theory. It was focus to observe about distance. The local partition dimension is an expansion of the partition dimension by adding certain conditions to the representation of the vertices ? to which is Π denoted by ?(?| Π). One of the conditions that must be met for ?(?| Π) is discussed. The minimum value of k so that there is a local distinguishing partition from V (G) is the local partition dimension of G or it can can be said that the distance of each neighbor is different. The local partition dimension of a graph G is denoted 〖pd〗_l (G). In this study, we used an axiomatic deductive methods and pattern recognition. In order to construct the discriminating set on the metric dimension (dim)  and the discriminating partition on the partition dimension (pd), the pattern detection method looks for patterns in which the coordinate values are minimum and different. By all observations, the local partition dimensions of  P_n×P_m Grid graph has two condition about the results of resolving partition. The Result of local partition dimension of a Grid graph 〖〖pd〗_l (P〗_n×P_m)=2, where n≥2 dan m≥2. In addition, it will decide how to convert the coordinates of areas in the Jember district that are prone to flooding and landslides into metric dimensions. It was about Coordinates of Flood and Landslide Disaster Locations in Jember Regency. The number of local and minimal partition sets generated for flood-prone areas in Jember Regency is 〖pd〗_l (G_Jember)=3.
Power Domination Number On Shackle Operation with Points as Lingkage Saifudin, Ilham
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (847.237 KB) | DOI: 10.31764/jtam.v4i1.1579

Abstract

The Power dominating set is a minimum point of determination in a graph that can dominate the connected dots around it, with a minimum domination point. The smallest cardinality of a power dominating set is called a power domination number with the notation . The purpose of this study is to determine the Shackle operations graph value from several special graphs with a point as a link. The result operation graphs are: Shackle operation graph from Path graph , Shackle operation graph from Sikel graph , Shackle operation graph from Star graph . The method used in this paper is axiomatic deductive method in solving problems. Understanding the axiomatic method itself is a method of deductive proof principles that applies in mathematical logic by using theorems that already exist in solving a problem. In this paper begins by determining the paper object that is the Shackle point operations result graph. Next, determine the cardinality of these graphs. After that, determine the point that has the maximum degree on the graph as the dominator point of power domination. Then, check whether the nearest neighbor has two or more degrees and analyze its optimization by using a ceiling function comparison between zero forching with the greatest degree of graph. Thus it can be determined ϒp minimal and dominated. The results of the power domination number study on Shackle operation graph result with points as connectors are , for  and ; , for  and ; , for  and .
Automatic Aircraft Navigation Using Star Metric Dimension Theory in Fire Protected Forest Areas Saifudin, Ilham; Umilasari, Reni
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 5, No 2 (2021): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v5i2.4331

Abstract

The purpose of this research is to determine the navigation of an unmanned aircraft automatically using theory of the metric dimension of stars in a forest fire area. The research will also be expanded by determining the star metric dimensions on other unique graphs and graphs resulting from amalgamation operations. The methods used in this research are pattern recognition and axiomatic deductive methods. The pattern detection method is to look for patterns to construct differentiated sets on the metric dimension (dim) so that the coordinate values are minimum and different. Meanwhile, axiomatic deductive is a research method that uses deductive proof principles that apply in mathematical logic by using existing axioms or theorems to solve a problem. Then the method is used to determine the stars' metric dimensions.
Co-Authors Afkar Ayyasy Amaliah, Ulfi Rizqi Arifianto, Deni Azhar, Reza Fachruddin Cinthia, Ella D. Dafik Dasuki, Moh. Fadhilah, Alvi Nur Ginanjar Abdurrahman Hartono, Ahmad Dedi Hidayat, Muhammad Hafid Hossain, Moch Minhas Husaini, Moh Isnawati Lujeng Lestari Lusiana, Dewi Makkulau, Andi Maulana, Oka Wahyu Mubaroq, Syahrul Muharom, Lutfi Ali Nanang Saiful Rizal Nurhalimah Nurhalimah Oktavianto, Hardian Rahman, Miftahur Ramadhani, Calvin Bahtiar Reza Fachruddin Azhar Rhomdani, Rohmad Wahid Rizky, Mohammad Rohman, Mucklis Aula Rojabi, Ilzam Samsurizal Samsurizal Suharso, Wiwik Taufiq Timur Warisaji Triawan Adi Cahyanto Triyanna Widiyaningtyas Umilasari, Reni Widjayanti, Fefi Nurdiana Wijaya, Guruh Yanuarti, Rosita Zakiyah, Amalina Maryam