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All Journal Journal of the Indonesian Mathematical Society Journal of Mathematics and Mathematics Education (JMME) Indonesian Journal of Combinatorics Jurnal Matematika UNAND Mattawang: Jurnal Pengabdian Masyarakat Jurnal Diferensial Tensor: Pure and Applied Mathematics Journal J-Icon : Jurnal Komputer dan Informatika
Ganesha L Putra
Universitas Nusa Cendana
Humanities Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Mathematics Public Health Social Sciences

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Journal : Jurnal Matematika UNAND

 1 
PELABELAN L(2, 1) PADA GRAF C_m ⊵_e C_n DAN S_m ⊵_o C_n Elisabet Lamapaha; Farly Oktriany Haning; Ganesha Lapenangga Putra
Jurnal Matematika UNAND Vol 13, No 2 (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.13.2.75-90.2024

Abstract

Diberikan $G$ suatu graf. Pelabelan $L(2,1)$ pada suatu graf $G$ merupakan suatu pemetaan $f: V(G)\rightarrow \mathbb{Z}^+\cup\{0\}$ sehingga untuk setiap $u,v\in V(G)$ dengan $d(u,v)=1$ atau $d(u,v)=2$  memenuhi syarat selisih label kedua titik setidaknya $3-d(u,v)$. Jika $k$ merupakan bilangan bulat terbesar yang digunakan, maka pelabelan $L(2,1)$ biasa ditulis dengan pelabelan $k$-$L(2,1)$. Selanjutnya, $\lambda_{2,1}(G)$ merupakan minimum nilai $k$ sehingga terdapat pelabelan $k$-$L(2,1)$ pada $G$. Pada penelitian ini, diberikan nilai $\lambda_{2,1}$ pada graf $C_m\unrhd_e C_n$ dan graf $S_m\unrhd_o C_n$.
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.
Co-Authors Ariyanto . Ariyanto Ariyanto Ataupah, Anthony Arthur Ci Manu Demetriana Kolo Elisabet Lamapaha Erika Feronika Br Simanungkalit Farly Oktriany Haning Gita N.A. Ginting Irvandi Gorby Pasangka Jeanete Y Nenabu Julieta Bernadita Adelia Radja Jusrry Rosalina Pahnael Keristina Br. Ginting Laura Erlinda Laidat Maria Agustina Kleden MARIA LOBO Meksianis Z Ndii Nurahmi Purnamasari - Pangaribuan, Rapmaida Megawaty Robertus Dole Guntur Salman A.N.M. Sarbaini Sarbaini Soewongsono, Junita Christine Sugi, Yoseph Syamsul Arifin Yosep Sugi