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All Journal Science and Technology Indonesia JMPM: Jurnal Matematika dan Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Limits: Journal of Mathematics and Its Applications Eksakta : Berkala Ilmiah Bidang MIPA Indonesian Journal of Combinatorics M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika Jurnal Matematika UNAND Jurnal Saintika Unpam : Jurnal Sains dan Matematika Unpam Warta Pengabdian Andalas: Jurnal Ilmiah Pengembangan Dan Penerapan Ipteks Jurnal Natural Limits: Journal of Mathematics and Its Applications
Des Welyyanti
Jurusan Matematika, FMIPA, Universitas Andalas
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Journal : M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika

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The Metric Dimension and Partition Dimension of The Amalgamation of Complete Graphs Abdurrahman, Fatih; Welyyanti, Des; Sandy, Ikhlas Pratama
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 10 No. 1 (2025): Mathline : Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v10i1.739

Abstract

In this paper, there is a section that identifies the aim of the research and makes it possible to suggest exploring the metric dimension and partition dimension of the amalgamation of complete graphs, which we would denote as Amal(Kn, v0)t. There are three steps conducted to achieve the research goals in this paper. To begin with, compute the lower bound of the metric dimension and the partition dimension of the graph Amal(Kn, v0)t. The second step is to find the upper bounds of the metric dimension and partition dimension of the graph Amal(Kn, v0)t by demonstrating that the representation of any vertex in Amal(Kn, v0)t is distinct. Finally, the exact values of the metric dimension and partition dimension of the graph Amal(Kn, v0)t are found if the lower and upper bounds are determined. The exact value of the metric dimension of the graph Amal(Kn, v0)t is denoted as dim(Amal(Kn, v0)t), while the exact value of the partition dimension is denoted as pd(Amal(Kn, v0)t). In this research, it is found that dim(Amal(Kn, v0)t) = (n - 2) for n, t ϵ N with n ≥ 3 and t ≥ 2. It is also found that pd(Amal(Kn, v0)t) = n for 2 ≤ t ≤ Cnn-1.
Co-Authors Abdi Musra Abdurrahman, Fatih Abel, Latifa Azhar ADEK HAYATI PUTRI Admi Nazra Afrianti Afrianti Aisyah Nurinsani Alifaziz Arsyad Alifaziz Arsyad Angryanof, Uthary Putri Budi Rudianto Citra Mayora Devianto, Dodi Efendi Efendi Effendi Effendi Eka Rahayu Nengsih A ELIZIA AUGUSTIN Elva Rahimah Fadhila Radiah Anas Fajri, Muhammad Rafif Fakhri Zikra Febria Angraini Fitri - Anggalia Hamdi, Muhammad Hazmira Yozza Ikhlas Pratama Sandy Kelson Novrianus Lessya KIKI KHAIRA MARDIMAR Laila Hidayati Laila Hidayati Mardimar, Kiki Khaira Mega Silvia Meiza Fiqrul Hanif MELATI NUR mellany mellany Muhammad Azhari Muhammad Rafif Fajri Muhammad Rafif Fajri MUHAMMAD RANDA Muthia Muhana Mutiara Ramadhani Syafnur Nada Andriani Nada Andriani Narwen Narwen Noverina Alfiany Nurinsani, Aisyah Permana, Dony REFI ALKADAR Rendy Aditya Pratama RUVIQA PUTRI SOLEHA Suci Rahma Putri Sugesti Sugesti Suhadi Wido Saputro SUTANTO, DASA Sutra Lidya Pritama Syafruddin . Tika Apriliza Uthary Putri Angryanof Yanita Yanita Yanuar, Ferra Yulianti, Lyra Zahara Zahara ZULKARNAIN, DEBI