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Ariyanto .
Program Studi Matematika Fakultas Sains Dan Teknik Universitas Nusa Cendana
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Engineering Health Professions Mathematics Mechanical Engineering Public Health Social Sciences Transportation

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Journal : Jurnal Matematika UNAND

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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 JARAK PADA GRAF HASIL KALI SISIR Soi Bau, Magdalena Clarita; Lapenangga Putra, Ganesha; Haning, Farly Oktriani; Aryanto
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.14.3.253-266.2025

Abstract

Diberikan graf tidak berarah $G= (V,E)$ dimana $V$ adalah himpunan simpul dan $E$ adalah himpunan sisi dari graf $G$. Graf $G$ merupakan graf dengan pelabelan anti ajaib jarak jika terdapat fungsi bijektif $f : V (G) \to \{1, 2, . . . , |V (G)|\}$ sehingga untuk setiap simpul u dan v, diperoleh $W(u)\neq W(v)$. Bobot titik $u \in V(G)$ didefinisikan sebagai $W(u)=\sum_{x\in N(u)} f(x)$ . Pada tulisan ini dibahas beberapa graf dengan operasi comb titik yang merupakan graf anti ajaib jarak. Hasilnya ialah pada beberapa kasus, graf $P_m \unrhd_o C_n,\; C_m \unrhd_o C_n,\; S_m \unrhd_o C_n,\; W_m \unrhd_o C_n,\; $ dan secara umum graf $G \unrhd_o C_n$ dan graf $G \unrhd_o W_n$ merupakan graf anti ajaib jarak.
Co-Authors Ade Martina Botha Kellen Albert Ch. Soewongsono Bernadinus Legimin Ganesha L Putra Haning, Farly Oktriani Irvandi Gorby Pasangka Jafaruddin Jafaruddin Julieta Bernadita Adelia Radja Keristina Br. Ginting Kumanireng, Albert Mario L. Putra, Ganesha Marabi Djala, Yusuf Betzelial Marlina Marine Meksianis Z Ndii Meksianis Zadrak Ndi Melania S Biri Mira Wadu Ndii, Meksianis Z Noldi Kasse Oktovianus Antonio Boleng Pangaribuan, Rapmaida M. Rapmaida M Pangaribuan Rapmaida M. Pangaribuan Rapmaida Megawaty Pangaribuan Soewongsono, Junita Christine Soi Bau, Magdalena Clarita Zakarias Seba Ngara