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Pangaribuan, Rapmaida Megawaty
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Computer Science & IT Mathematics

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ZONAL LABELING OF EDGE COMB PRODUCT OF GRAPHS Soewongsono, Junita Christine; Putra, Ganesha Lapenangga; Ariyanto, Ariyanto; Pangaribuan, Rapmaida Megawaty
Jurnal Matematika UNAND Vol. 13 No. 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.388-395.2024

Abstract

Given a plane graph $G=(V,E)$. A zonal labeling of graph $G$ is defined as an assignment of the two nonzero elements of the ring $\mathbb{Z}_3$, which are $1$ and $2$, to the vertices of $G$ such that the sum of the labels of the vertices on the border of each region of the graph is $0\in\mathbb{Z}_3$. A graph $G$ that possess such a labeling is termed as zonal graph. This paper will characterize edge comb product graphs that are zonal. The results show that $P_m\trianglerighteq_eC_n$, $C_n\trianglerighteq_e C_r$, $S_p\trianglerighteq_e C_n$, and $S_p\trianglerighteq_e F_t$ are zonal in some cases, but not in others.
PELABELAN ANTI AJAIB PADA GRAF HASIL KALI SISIR Liunokas, Mariance Crisatya; Lapenangga Putra, Ganesha; Pangaribuan, Rapmaida Megawaty; Pasangka, Irvandi Gorby
Jurnal Matematika UNAND Vol. 14 No. 3 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.3.240-252.2025

Abstract

Suatu graf $G$ dikatakan graf anti ajaib jika memuat pelabelan anti ajaib, yaitu $f : E(G) \rightarrow \{1,2,…, |E(G)|\}$ merupakan fungsi bijektif, dan untuk setiap simpul memiliki nilai bobot yang berbeda. Dalam tulisan ini, terdapat beberapa pelabelan anti ajaib dengan menggunakan operasi hasil kali sisir, dan hasilnya adalah graf $C_m \unrhd_o C_n, P_m \unrhd_o C_n, S_m \unrhd_o C_n, W_m \unrhd_o C_n$ dan secara umum untuk $G$ suatu graf terhubung dan $r-reguler$, $ G\unrhd_oC_n$ merupakan graf anti ajaib. A graph $G$ is said to be antimagic if it contains an antimagic label, that is, $f : E(G) \rightarrow \{1,2,…, |E(G)|\}$ is a bijective function, and each vertex has a different weight value. In this paper, there are several anti-magic labelings using the comb product operation and the results are the graphs $C_m \unrhd_o C_n, P_m \unrhd_o C_n, S_m \unrhd_o C_n, W_m \unrhd_o C_n$ and in general for $G$ a connected and $r-regular$ graph, $ G\unrhd_oC_n$ is an anti-magic graph.
Co-Authors Ariyanto Ariyanto Ganesha L Putra Irvandi Gorby Pasangka Liunokas, Mariance Crisatya Soewongsono, Junita Christine