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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 strong 3-rainbow index of edge-comb product of a path and a connected graph Zata Yumni Awanis; A.N.M. Salman; Suhadi Wido Saputro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.3

Abstract

Let G be a connected and edge-colored graph of order n, where adjacent edges may be colored the same. A tree in G is a rainbow tree if all of its edges have distinct colors. Let k be an integer with 2 ≤ k ≤ n. The minimum number of colors needed in an edge coloring of G such that there exists a rainbow tree connecting S with minimum size for every k-subset S of V(G) is called the strong k-rainbow index of G, denoted by srxk(G). In this paper, we study the srx3 of edge-comb product of a path and a connected graph, denoted by Pno⊳eH. It is clearly that |E(Pno⊳eH)| is the trivial upper bound for srx3(Pno⊳eH). Therefore, in this paper, we first characterize connected graphs H with srx3(Pno⊳eH)=|E(Pno⊳eH)|, then provide a sharp upper bound for srx3(Pno⊳eH) where srx3(Pno⊳eH)≠|E(Pno⊳eH)|. We also provide the exact value of srx3(Pno⊳eH) for some connected graphs H.
KARAKTERISTIK STRUKTUR KOMUNITAS MAKROZOOBENTOS DI PERAIRAN EKOSISTEM MANGROVE GILI LAWANG, LOMBOK TIMUR Niechi Valentino; Sitti Latifah; Budhy Setiawan; Eni Hidayati; Zata Yumni Awanis; Hayati Hayati
Jurnal Belantara Vol 5 No 1 (2022)
Publisher : Forestry Study Program University Of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1170.342 KB) | DOI: 10.29303/jbl.v5i1.888

Abstract

The role of the mangrove ecosystem as an ecological link through high productivity compared to other ecosystems has had a major impact on the existence of the mangrove ecosystem distribution. This study aims to find out the type of organic ingredient content and abundance of macrozoobenthos and find out the relationship of organic ingredient content to the abundance of macrozoobenthos. The research was carried out in November 2021 using a purposive sampling technique method with a total of 5 stations. The samples taken were the sediments substrate and macrozoobenthos. The results shown that the organic content is dominated by saturated textures, muddy sand textures and saturated clay textures with an average organic content ranging from 1.24% - 1.90%. There were 15 types of macrozoobenthos found and dominated by the Gastropod class with an average abundance of macrozoobenthos ranging from 202 ind/m2 - 525 ind/m2. The types of macrozoobenthos found were Nassarius distortus, Anadara sp, Mesodesma sp, Mytillus sp, Donax sp, Abra soyoae, Cerithideopsilla djadjariensis, Telescopium telescopium, Cassidula nucleus, Cassidula angulifera, Litttoridina sp., Potamopyrgus sp., Melanoides sp., Battilaria zonalis dan Lumbriculus sp. The effect of organic matter content on the abundance of macrozoobenthos by 10.7% and 89.3% was more influenced by physic-chemical factors in Gili Lawang waters.
Rainbow connection number of comb product of graphs Dinny Fitriani; ANM Salman; Zata Yumni Awanis
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.9

Abstract

An edge-colored graph G is called a rainbow connected if any two vertices are connected by a path whose edges have distinct colors. Such a path is called a rainbow path. The smallest number of colors required in order to make G rainbow connected is called the rainbow connection number of G. For two connected graphs G and H with v ∈ V(H), the comb product between G and H, denoted by G⊳vH, is a graph obtained by taking one copy of G and |V(G)| copies of H and identifying the i-th copy of H at the vertex v to the i-th vertex of G. In this paper, we give sharp lower and upper bounds for the rainbow connection number of comb product between two connected graphs. We also determine the exact values of rainbow connection number of G⊳vH for some connected graphs G and H.
PELATIHAN PEMBUATAN KUIS INTERAKTIF DENGAN APLIKASI QUIZIZZ DALAM PEMBELAJARAN MATEMATIKA Jurnal Pepadu; Ni Wayan Switrayni; I Gede Adhitya Wisnu Wardhana; Irwansyah Irwansyah; Qurratul Aini; Salwa Salwa; Zata Yumni Awanis; Fariz Maulana
Jurnal Pepadu Vol. 4 No. 1 (2023): Jurnal Pepadu
Publisher : LPPM UNIVERSITAS MATARAM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/pepadu.v4i1.2244

Abstract

Akhir-akhir ini pembelajaran dalam beberapa jenjang pendidikan dilakukan dengan sistem blended learning yaitu memadukan pembelajaran daring dan luring. Dalam kombinasi proses pembelajaran tersebut guru masih kesulitan memberikan materi dan evaluasi pembelajaran matematika yang interaktif dan menyenangkan. Masalah ini dialami pula oleh para guru di Madrasah Aliyah Manhalul Ma’arif. Oleh karena itu, untuk mengatasi masalah tersebut, kegiatan Pengabdian Kepada Masyarakat ini bertujuan untuk mengenalkan para guru Madrasah Aliyah Manhalul Ma’arif khususnya untuk guru matematika dengan pembuatan slide pembelajaran dan kuis interaktif menggunakan aplikasi Quizizz. Adapun metode yang digunakan adalah dalam bentuk pelatihan secara luring. Pelaksanaan Kegiatan Pengabdian Kepada Masyarakat ini sudah berjalan dengan cukup baik dan lancar. Para guru sangat antusias dalam proses pelatihan dan merasakan bahwa kegiatan ini bermanfaat bagi mereka dalam menyusun slide pembelajaran matematika yang interaktif. Dapat disimpulkan bahwa melalui pelatihan ini, para guru Madrasah Aliyah Manhalul Ma’arif sudah mengenal dan mampu menciptakan materi pembelajaran matematika dalam bentuk slide pembelajaran dan quiz interaktif dan menyenangkan bagi para siswa menggunakan aplikasi Quizizz.
Optimization of water flow on Regency Municipality Waterworks-network of Jonggat Central Lombok Regency using Ford Fulkerson Algorithm and Dinic Algorithm Lilis Sriwahyuni; Marwan Marwan; Zata Yumni Awanis
Eigen Mathematics Journal Vol. 6 No. 1 Juni 2023
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v6i1.157

Abstract

Clean water is essential for humans which must be fulfilled for humans survival. The population in Jonggat, Central Lombok, increases from year to year which causes the using of clean water get an increase too. The necessity of rising clean water is not in line with the availability of water in nature, therefore the PDAM (Regency Municipality Waterworks) manages existing water resource. Then, it will be distributed to consumers. The purpose of this research is to determine the optimal solution in the distribution of clean water in Jonggat using Ford Fulkerson algorithm and Dinic algorithm. Both Ford Fulkerson algorithm and Dinic algorithm are methods used to calculate the maximum flow in a network. Based on the results of research using Python software on the Ford Fulkerson algorithm, the maximum current is 133 liters/second, while using the Dinic algorithm, the maximum current is 133.49 liters/second. Meanwhile, the average water flow is delivered by PDAM is 95 liters/second. It means, it can be added the amount of flow in the clean water distribution pipe by the PDAM. It’s for facilitating the flow of water that reaches consumers with the addition of a flow that cannot exceed 133.49 liters/second. Keywords: Network flow, Maximum flow, Ford Fulkerson algorithm, Dinic algorithm
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.
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.
Graf Nilpoten Dari Gelanggang Bilangan Bulat Modulo Berorde Pangkat Prima Malik, Deny Putra; Wardhana, I Gede Adhitya Wisnu; Dewi, Putu Kartika; Widiastuti, Ratna Sari; Maulana, Fariz; Syarifudin, Abdul Gazir; Awanis, Zata Yumni
JMPM: Jurnal Matematika dan Pendidikan Matematika Vol 8 No 1 (2023): March - August 2023
Publisher : Prodi Pendidikan Matematika Universitas Pesantren Tinggi Darul Ulum Jombang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26594/jmpm.v8i1.2920

Abstract

Nilpotent graph of ring integer modulo is one of the graph representations in algebraic structures. This study aims to find out the shape and properties of a nilpotent graph of ring prime numbers modulo which is then generalized to a ring of integers modulo with arbitrary prime power. The method used in this research is a literature study. In the ring of integer modulo, we get the shape of a nilpotent graph as a star graph. Then, the characteristic of a nilpotent graph on a ring integer modulo with arbitrary prime power is that it contains a complete subgraph and contains a number of as a star subgraph.
THE POWER GRAPH REPRESENTATION FOR INTEGER MODULO GROUP WITH POWER PRIME ORDER Putra, Lalu Riski Wirendra; Awanis, Zata Yumni; Salwa, Salwa; Aini, Qurratul; Wardhana, I Gede Adhitya Wisnu
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 3 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss3pp1393-1400

Abstract

There are many applications of graphs in various fields. Starting from chemical problems, such as the molecular shape of a compound to internet network problems, we can also use graphs to depict the abstract concept of a mathematical structure.. Groups in Algebra can be represented as a graph. This is interesting because Groups are abstract objects in mathematics. The graph of a group shows the physical form of the group by looking at the relationship between its elements. So, we can know the distance of the elements. In 2013, Abawajy et al. conducted studies related to power graphs. Power graph representation of groups of integers modulo with the order of prime numbers has been carried out in 2022 by Syechah, et al. In this article, the author provides the properties of a power graph on a group of integers modulo with the order of powers of prime numbers.
Super (a,d)-P_2⨀P_m-Antimagic Total Labeling of Corona Product of Two Paths Yatin, Bela Zainun; Awanis, Zata Yumni; Wardhana, I Gede Adhitya Wisnu
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.v8i2.20065

Abstract

Graph labeling involves mapping the elements of a graph (edges and vertices) to a set of positive integers. The concept of an anti-magic super outer labeling (a,d)-H pertains to assigning labels to the vertices and edges of a graph using natural numbers {1,2,3,...,p+q}. The weights of the outer labels H form an arithmetic sequence {a,a+d,a+2d,...,a+(k-1)d}, where 'a' represents the first term, 'd' is the common difference, and 'k' denotes the total number of outer labels, with the smallest label assigned to a vertex. This study investigates the super (a,d)-P_2⨀P_m-antimagic total labeling of the corona product P_n⨀P_m, where n and m are both greater than or equal to 3. We define the labeling functions for vertices and edges based on the partitioning of labels into three subsets. Using k-balanced and (k,δ)-anti balanced multisets, we demonstrate that for m being odd, P_n⨀P_m is super (9m^2 n+4mn+m-n+3,1)-P_2 ⨀▒P_(m ) -antimagic, and for m being even, P_n⨀P_m is super (9m^2 n+4mn+m-2n+5,3)-P_2 ⨀▒P_(m ) -antimagic. The labeling scheme is illustrated through examples. For the case when m is odd, an antimagic total labeling of P_3 ⨀▒P_3    forms a super (282,1)- P_2 ⨀▒P_(3 )  -antimagic labeling. In the case of even m, an antimagic total labeling of P_3 ⨀▒P_(4 ) results in a super (483,3)- P_2 ⨀▒P_(4 )  -antimagic labeling. Both of these examples provide insights into the antimagic properties of corona products.
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