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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) JMPM: Jurnal Matematika dan Pendidikan Matematika Jurnal Belantara BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) EIGEN MATHEMATICS JOURNAL InPrime: Indonesian Journal Of Pure And Applied Mathematics Jurnal Diferensial Jurnal Pepadu Semeton Mathematics Journal Sinergi dan Harmoni Masyarakat MIPA
Zata Yumni Awanis
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, University Of Mataram, Jalan Majapahit No. 62, Mataram 83125, Indonesia
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The Topological Indices of Coprime Graph for Integer Module Group Abdurahim, Abdurahim; Awanis, Zata Yumni; Syechah, Bulqis Nebulla; Syaharuddin, Syaharuddin
JURNAL DIFERENSIAL Vol 6 No 2 (2024): November 2024
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v6i2.14816

Abstract

This study delves into the fascinating realm of coprime graphs within the integer modulo group, revealing a fundamental property where these graphs manifest as star graphs when the order corresponds to a prime power. This pivotal insight, as elucidated by [1], plays a crucial role in the determination of topological indices for these graphs. The research culminates in the formulation of formulas for the First Zagreb index and the Second index of coprime graphs in the context of integer modulo groups, unveiled in the last two theorems. These numerical topological indices are poised to unveil intricate correlations among group elements, contingent upon their order, echoing the foundational principles of chemical graph theory. This exploration not only enriches our understanding of group structu.Coprime Graph
Penerapan Pusat Dan Pusat Berat Graf Dalam Penentuan Lokasi Strategis Pembangunan Fasilitas Umum Di Pulau Lombok Lata, Nandha Waldana; Awanis, Zata Yumni; Aini, Qurratul
Semeton Mathematics Journal Vol 1 No 1 (2024): April
Publisher : Program Studi Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/semeton.v1i1.225

Abstract

Determining a strategic location in a region can be done using the Center and Centroid of a graph. This involves transforming a region's map into a graph form, then identifying the center and centroid of the graph. The determination of the centroid is done by identifying the minimum spanning tree of the graph using Kruskal's and Prim's algorithms. In this study, strategic location determination was carried out to find suitable places for constructing public facilities such as hospitals, schools, and others on Lombok Island. The results showed that Lenek, Pringgasela, and Suralaga Districts are the most strategic areas in Lombok Timur Regency for building public facilities. For other regencies, namely Lombok Tengah, Lombok Barat, Lombok Utara, and the city of Mataram, one strategic location was found in each, specifically in Praya District, Kediri District, Gangga District, and Selaparang District, respectively.
The Clique Number and The Chromatics Number Of The Coprime Graph for The Generalized Quarternion Group Gayatri, Marena Rahayu; Nurhabibah, Nurhabibah; Aini, Qurratul; Awanis, Zata Yumni; Salwa, Salwa; Wardhana, I Gede Adhitya Wisnu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 2 (2023): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i2.13099

Abstract

Graph theory can give a representation of abstract mathematical systems such as groups or rings. We have many graph representations for a group, in this study we use the coprime graph representation for a generalized quaternion group to find the numerical invariants of the graph, which are the clique number and the chromatic number. The main results obtained from this study are the clique number of the coprime graph representation for the generalized quaternion group is equal to the chromatic number of the coprime graph representation for the generalized quaternion group for each case of  the order.
Implementasi Modul Olimpiade SMP Di SMPN 2 Kuripan Lombok Barat Putra, Lalu Riski Wirendra; Pratama, Rendi Bahtiar; Karang, Gusti Yogananda; Irwansyah, Irwansyah; Wardhana, I Gede Adhitya Wisnu; Romdhini, Mamika Ujianita; Abdurahim, Abdurahim; Maulana, Fariz; Satriyantara, Rio; Awanis, Zata Yumni; Putri, Syaftirridho; Graha, Syifa Salsabila Satya; Wahidah, Fathul Maulina; Pratiwi, Lia Fitta; Pradana, Satriawan; Siboro, Ayes Malona; Farwan, Farwan
Sinergi dan Harmoni Masyarakat MIPA Vol. 1 No. 1 (2024): Oktober
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/sinonim.v1i1.5517

Abstract

Kegiatan pengabdian kepada masyarakat ini bertujuan untuk mengimpelementasikan modul pembelajaran olimpiade matematika bagi siswa SMPN 2 Kuripan. Kebutuhan akan modul ini didasarkan pada rendahnya akses siswa terhadap materi-materi persiapan olimpiade yang terstruktur dan sesuai dengan kemampuan serta kebutuhan mereka. Metode yang digunakan dalam pengembangan modul ini meliputi analisis kebutuhan, desain dan pengembangan modul, serta uji coba. Modul ini dirancang untuk mencakup berbagai topik matematika yang sering muncul dalam olimpiade, disertai dengan contoh soal dan pembahasan yang mendalam. Hasil dari kegiatan ini menunjukkan bahwa penggunaan modul olimpiade matematika ini dapat meningkatkan pemahaman siswa terhadap materi olimpiade, serta memotivasi mereka untuk lebih aktif dalam mengikuti kompetisi. Evaluasi melalui uji coba menunjukkan respon positif dari siswa, dengan peningkatan signifikan pada hasil latihan soal.
Social Network Analysis of Twitter Users on BTS Topic Using Degree Centrality, Betweenness Centrality, and Closeness Centrality Adniati, Siti; Irwansyah, Irwansyah; Awanis, Zata Yumni
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 2 (2023)
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.v5i2.28722

Abstract

AbstractNowadays, a trademark is starting to be built through content on social media by involving influencers whose roles are increasingly needed in digital marketing. Hence, finding them on social media networks is an important thing. In brand recognition, BTS has a great influence where a brand they collaborate with gets an enthusiastic response from fans who participate in disseminating information and recommending it to others via Twitter. Therefore, this study aims to identify the potential influencer on the delivery of information on the topic of BTS on Twitter using social network analysis. Social network analysis applies the concept of graph theory where the potential influencer which is denoted by the central vertex is measured by measures of centrality, namely degree centrality, betweenness centrality, and closeness centrality. The result of the network consists of 649 vertices and 730 directed edges that form a disconnected and directed network with 67 weakly connected components. This study indicates that the influencers in the network can be fan accounts or fanbase accounts.Keywords: BTS; centrality; central vertex; influencer; social network analysis; Twitter. AbstrakDewasa ini, suatu merek dagang mulai dibangun  melalui konten di media sosial dengan melibatkan pemengaruh yang perannya semakin dibutuhkan pada pemasaran digital sehingga menemukan mereka di jaringan media sosial adalah suatu hal yang penting. Dalam pengenalan merek, BTS memberikan pengaruh yang besar dimana suatu merek yang berkolaborasi dengan mereka mendapat respon antusias dari penggemar yang ikut menyebarluaskan informasi dan merekomendasikannya kepada orang lain melalui Twitter. Oleh karena itu, penelitian ini bertujuan untuk mengidentifikasi pemengaruh potensial dalam penyampaian informasi pada topik BTS di Twitter menggunakan analisis jaringan sosial. Analisis jaringan sosial menerapkan konsep teori graf dimana simpul sentral diukur dengan ukuran sentralitas, yaitu sentralitas derajat, sentralitas keantaraan, dan sentralitas kedekatan. Diperoleh jaringan dengan 649 simpul dan 730 sisi berarah yang membentuk jaringan berarah tak terhubung yang terdiri atas 67 komponen terhubung lemah. Adapun hasil dari penelitian ini menunjukkan bahwa simpul sentral atau pemengaruh dalam jaringan dapat berupa akun personal dari pengemar (fan account) atau akun basis penggemar (fanbase).Kata Kunci: analisis jaringan  sosial, BTS,  pemengaruh , sentralitas, simpul sentral, Twitter. 2020MSC: 05C90, 91D30.
The Strong 3-Rainbow Index of Graphs Containing Three Cycles Awanis, Zata Yumni
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 1 (2023)
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.v5i1.29133

Abstract

AbstractThe concept of a strong k-rainbow index is a generalization of a strong rainbow connection number, which has an interesting application in security systems in a communication network. Let G be an edge-colored connected graph of order n, where adjacent edges may be colored the same. A rainbow tree in G is a tree whose edges have distinct colors. For an integer k with 2≤k≤n, the strong k-rainbow index srx_k (G) of G is the minimum number of colors needed to color all edges of G so that every k vertices of G are connected by a rainbow tree of minimum size. We focus on k=3. It is clear that srx_3 (G)≤‖G‖, where the upper bound is sharp since the srx_3 of a tree equals its size. Hence, we are interested in studying how the srx_3 of a tree changes if we add some edges connecting two nonadjacent vertices in the tree. This paper is focused on graphs containing three cycles. We first determine a sharp upper bound of the srx_3 of graphs containing exactly three edge-disjoint cycles. We also determine the exact values of srx_3 of theta graph θ(a_1,a_2,a_3) for certain values of a_1, a_2, and a_3.Keywords: cycle; rainbow coloring; rainbow Steiner tree; theta graph; tree. AbstrakKonsep indeks pelangi-k kuat merupakan perumuman dari bilangan terhubung pelangi kuat yang memiliki aplikasi menarik dalam sistem keamanan jaringan komunikasi. Misalkan G adalah suatu graf terhubung berorde n yang memiliki suatu pewarnaan sisi, dimana dua sisi bertetangga boleh memiliki warna yang sama. Pohon pelangi di G adalah pohon yang setiap sisinya memiliki warna berbeda. Untuk suatu bilangan bulat k dengan 2≤k≤n, indeks pelangi-k kuat srx_k (G) graf G adalah banyak warna minimum yang dibutuhkan untuk mewarnai semua sisi di G sehingga setiap k titik di G dihubungkan oleh suatu pohon pelangi berukuran minimum. Kami fokus pada k=3. Jelas bahwa srx_3 (G)≤‖G‖, dimana batas atas ini merupakan batas ketat karena srx_3 pohon sama dengan ukurannya. Karena itu, kami tertarik untuk mempelajari bagaimana srx_3 pohon berubah jika ditambahkan beberapa sisi yang menghubungkan dua titik tidak bertetangga di pohon tersebut. Artikel ini difokuskan pada graf yang memuat tiga siklus. Pertama, kami menentukan batas atas ketat srx_3 graf yang memuat tepat tiga siklus saling lepas sisi. Kami juga menentukan nilai eksak srx_3 graf theta θ(a_1,a_2,a_3 ) untuk beberapa nilai a_1, a_2, dan a_3 tertentu.Kata Kunci: siklus; pewarnaan pelangi; pohon Steiner pelangi; graf theta; pohon. 2020MSC: 05C05, 05C15, 05C38, 05C40.
Co-Authors A.N.M. Salman Abdul Gazir Syarifudin Abdurahim, Abdurahim Adniati, Siti ANM Salman Dewi, Putu Kartika Dinny Fitriani Eni Hidayati Farwan, Farwan Gayatri, Marena Rahayu Graha, Syifa Salsabila Satya Hayati Hayati I Gede Adhitya Wisnu Wardhana Irwansyah Irwansyah Irwansyah Irwansyah Jurnal Pepadu Karang, Gusti Yogananda Lata, Nandha Waldana Lilis Sriwahyuni Malik, Deny Putra Mamika Ujianita Romdhini, Mamika Ujianita Marwan Marwan Maulana, Fariz Ni Wayan Switrayni Niechi Valentino Nurhabibah Nurhabibah Pradana, Satriawan Pratama, Rendi Bahtiar Pratiwi, Lia Fitta Putra, Lalu Riski Wirendra Putri, Syaftirridho Qurratul Aini Qurratul Aini Rio Satriyantara Salwa Salwa Salwa Salwa Setiawan, Budhy Siboro, Ayes Malona Sitti Latifah Suhadi Wido Saputro Syaharuddin Wahidah, Fathul Maulina Widiastuti, Ratna Sari Yatin, Bela Zainun