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All Journal Jurnal Edukasi Universitas Jember KADIKMA CAUCHY: Jurnal Matematika Murni dan Aplikasi EDU-MAT: Jurnal Pendidikan Matematika Unisda Journal of Mathematics and Computer Science (UJMC) JTAM (Jurnal Teori dan Aplikasi Matematika) Warta Pengabdian JURNAL AXIOMA : Jurnal Matematika dan Pembelajaran JPKMI (Jurnal Pengabdian Kepada Masyarakat Indonesia) Contemporary Mathematics and Applications (ConMathA) Jurnal Ilmu Pendidikan Sekolah Dasar CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS JAMAIKA: Jurnal Abdi Masyarakat Pancaran Pendidikan
Robiatul Adawiyah
Program Studi Pendidikan Matematika, Universitas Jember, Jember, Indonesia
Agriculture, Biological Sciences & Forestry Humanities Chemistry Computer Science & IT Economics, Econometrics & Finance Education Environmental Science Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Physics Public Health Social Sciences Other

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DIMENSI METRIK SISI PADA KELUARGA GRAF TANGGA Adawiyah, Robiatul; Prihandini, Rafiantika Megahnia
Kadikma Vol 12 No 1 (2021): April 2021
Publisher : Department of Mathematics Education , University of Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/kdma.v12i1.24810

Abstract

Misalkan G adalah graf terhubung dan sederhana, dinotasikan sebagai , dengan adalah himpunan titik dan adalah sebuah sisi. Jarak antara titik v dan sisi e dinotasikan sebagai Titik membedakan dua sisi jika Himpunan titik W dari graf terhubung G adalah generator dimensi metrik sisi pada G jika untuk setiap dua sisi dari G dibedakan oleh beberapa titik dari . Dimensi metrik sisi merupakan kardinalitas minimum dari semua genetor dimensi metrik sisi pada G yang dilambangkan dengan . Pada Penelitian ini, akan diteliti dimensi metrik sisi pada beberapa keluarga graf tangga yaitu graf tangga dan graf tangga miring untuk
Metric Coloring of Pencil Graphs Adawiyah, Robiatul; Pujiyanto, Arif; Kristiana, Arika Indah; Dafik, Dafik; Prihandini, Rafiantika Megahniah; Susanto, Susanto
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27242

Abstract

A graph is defined as an ordered pair (V,E), where V is a non-empty set of elements called vertices, and E is a set of edges that are finite and may be empty. Each edge connects two distinct vertices from V(G). Let f:V(G)→{1,2,3,…,k} be a coloring of the vertices of graph G, where two adjacent vertices can be colored with the same color. Considering the set of color classes Π={C_1,C_2,…,C_k}, for a vertex v in G, the color representation of v is a k-vector r(Π)=(d(v,C_1 ),d(v,C_2 ),…,d(v,C_k )),, where d(v,C_1 )=min⁡{d(v,c)∶c∈C_1}. If r(u | Π )≠r(v | Π ) for every two adjacent vertices u and v in G, the coloring is called a metric coloring of G. Thus, it can be concluded that two adjacent vertices u and v can be colored with the same color if their metric code conditions are different. The minimum number of the metric coloring is called as metric chromatic number. The goal of this research is analizing the metric chromatic number of the pencil graph. This graph was chosen because no previous research had been carried out on this graph. The proof begins by determining the lower bound, then determining the upper bound by checking coloring function and checking the metric coloring function and the metric code function of each vertex. In this research, we got the exact value of metric chromatic number of several type of pencil graph.
Co-Authors Antonius Cahya Prihandoko Arika Indah Kristiana Arika Indah Kristiana D. Dafik Dafik Elsa Yuli Kurniawati Ermita Rizki Albirri Ermita Rizki Albirri I Made Tirta Indi Izzah Makhfduloh Inge Wiliandani Setya Putri Khilyah Munawaroh Lioni Anka Monalisa, Lioni Anka Muhammad Gufronil Halim Muhammad Lutfi Asy’ari Mutiara Bilqis Nabilah Ayu Az-Zahra Nuwaila Izzatul Muttaqi Prihandini, Rafiantika Megahniah Pujiyanto, Arif Qurrota A'yuni Ar Ruhimat Qurrotul A’yun Rafelita Faradila Sandi Rafiantika Megahnia Rafiantika Megahnia Prihandini Rafiantika Megahniah Prihandini Reza Ambarwati Ridho Alfarisi S Slamin Saddam Hussen Slamin Slamin Slamin Susanto Susanto Tawakal, Anzori Zainur Rasyid Ridlo