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All Journal Bulletin of Electrical Engineering and Informatics Journal of the Indonesian Mathematical Society Desimal: Jurnal Matematika Jurnal Matematika UNAND Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya
Edy Tri Baskoro
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
Computer Science & IT Education Electrical & Electronics Engineering Mathematics Social Sciences

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Penelitian Matematika untuk Kemajuan Bangsa Baskoro, Edy Tri
Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya 2016: Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya
Publisher : Universitas Muhammadiyah Surakarta

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Abstract

1. Motivasi: Mengapa perlu penelitian matematika?2.Apa itu Matematika?3.Perkembangan matematika di Indonesia4.Peranan Matematika dalam membangun bangsa
KARAKTERISASI POHON DENGAN BILANGAN DOMINASI-LOKASI-METRIK TIGA Zulfaneti, Zulfaneti; Baskoro, Edy Tri; Assiyatun, Hilda
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.13.4.340-348.2024

Abstract

Misalkan G = (V;E) adalah graf sederhana dan terhubung. Untuk suatu himpunan R = fr1; r2; : : : ; rkg V dan v 2 V , representasi titik v terhadap R adalah vektor r(vjR) = (d(v; r1); d(v; r2); : : : ; d(v; rk)) dimana d(v; r) menyatakan jarak titik v dan titik r. Himpunan R disebut himpunan pembeda dari G jika semua titik di G memiliki representasi unik terhadap R. Himpunan D disebut himpunan dominasi dari G jikasetiap titik di G-D bertetangga dengan suatu titik v 2 D. Suatu himpunan dominasidan juga merupakan himpunan pembeda disebut himpunan dominasi-lokasi-metrik dariG. Kardinalitas dari himpunan dominasi-lokasi-metrik minimum dari G disebut bilangan dominasi-lokasi-metrik dari G. Semua graf orde n dengan bilangan dominasi-lokasi-metrik 1, 2, n-2 dan n-3 telah ditentukan secara lengkap. Dalam tulisan ini, kamimengkarakterisasi semua pohon dengan bilangan-dominasi-lokasi-metrik 3 dan secarakhusus membuktikan bahwa tidak ada pohon dengan bilangan-dominasi-lokasi-metriksama dengan dimensi metriknya.
KARAKTERISASI POHON DENGAN BILANGAN DOMINASI-LOKASI-METRIK TIGA Zulfaneti, Zulfaneti; Baskoro, Edy Tri; Assiyatun, Hilda
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.13.4.340-348.2024

Abstract

Misalkan G = (V;E) adalah graf sederhana dan terhubung. Untuk suatu himpunan R = fr1; r2; : : : ; rkg V dan v 2 V , representasi titik v terhadap R adalah vektor r(vjR) = (d(v; r1); d(v; r2); : : : ; d(v; rk)) dimana d(v; r) menyatakan jarak titik v dan titik r. Himpunan R disebut himpunan pembeda dari G jika semua titik di G memiliki representasi unik terhadap R. Himpunan D disebut himpunan dominasi dari G jikasetiap titik di G-D bertetangga dengan suatu titik v 2 D. Suatu himpunan dominasidan juga merupakan himpunan pembeda disebut himpunan dominasi-lokasi-metrik dariG. Kardinalitas dari himpunan dominasi-lokasi-metrik minimum dari G disebut bilangan dominasi-lokasi-metrik dari G. Semua graf orde n dengan bilangan dominasi-lokasi-metrik 1, 2, n-2 dan n-3 telah ditentukan secara lengkap. Dalam tulisan ini, kamimengkarakterisasi semua pohon dengan bilangan-dominasi-lokasi-metrik 3 dan secarakhusus membuktikan bahwa tidak ada pohon dengan bilangan-dominasi-lokasi-metriksama dengan dimensi metriknya.
Characterization of \mathcal{R}(2K_2,F_n) with Minimum Order for Small n Fajri, Muhammad Rafif; Assiyatun, Hilda; Baskoro, Edy Tri
Journal of the Indonesian Mathematical Society Vol. 31 No. 2 (2025): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i2.1871

Abstract

A Fan graph $F_n$ is defined as the graph $P_n+K_1$, where $P_n$ is the path on $n$ vertices. The notation $F \rightarrow (G, H)$ means that if all edges of $F$ are arbitrarily colored by red or blue, then either the subgraph of $F$ induced by all red edges contains a graph $G$ or the subgraph of $F$ induced by all blue edges contains a graph $H.$ Let $\mathcal{R}(G, H)$ denote the set of all graphs $F$ satisfying $F \rightarrow (G, H)$ and for every $e \in E(F),$ $(F - e) \not\rightarrow (G, H).$ In this paper, we propose some properties for a graph $G$ of minimum order that belongs to $\mathcal{R}(2K_2,F_n),$ for $n \geq 3$. We have also found all members of $\mathcal{R}(2K_2,F_n)$ with a minimum order for $n \in [3,7]$.
Partition dimension of disjoint union of complete bipartite graphs Haryeni, Debi Oktia; Baskoro, Edy Tri; Saputro, Suhadi Wido
Desimal: Jurnal Matematika Vol. 4 No. 2 (2021): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v4i2.10190

Abstract

For any (not necessary connected) graph $G(V,E)$ and $A\subseteq V(G)$, the distance of a vertex $x\in V(G)$ and $A$ is $d(x,A)=\min\{d(x,a): a\in A\}$. A subset of vertices $A$ resolves two vertices $x,y \in V(G)$ if $d(x,A)\neq d(y,A)$. For an ordered partition $\Lambda=\{A_1, A_2,\ldots, A_k\}$ of $V(G)$, if all $d(x,A_i)<\infty$ for all $x\in V(G)$, then the representation of $x$ under $\Lambda$ is $r(x|\Lambda)=(d(x,A_1), d(x,A_2), \ldots, d(x,A_k))$. Such a partition $\Lambda$ is a resolving partition of $G$ if every two distinct vertices $x,y\in V(G)$ are resolved by $A_i$ for some $i\in [1,k]$. The smallest cardinality of a resolving partition $\Lambda$ is called a partition dimension of $G$ and denoted by $pd(G)$ or $pdd(G)$ for connected or disconnected $G$, respectively. If $G$ have no resolving partition, then $pdd(G)=\infty$. In this paper, we studied the partition dimension of disjoint union of complete bipartite graph, namely $tK_{m,n}$ where $t\geq 1$ and $m\geq n\geq 2$. We gave the necessary condition such that the partition dimension of $tK_{m,n}$ are finite. Furthermore, we also derived the necessary and sufficient conditions such that $pdd(tK_{m,n})$ is either equal to $m$ or $m+1$.
Vertex and edge labelling strategies for graph-based computed tomography image denoising Setiawan, Iwan; Rosiyadi, Didi; Ratianingsih, Rina; Abu, Maulidyani; Baskoro, Edy Tri
Bulletin of Electrical Engineering and Informatics Vol 15, No 2: April 2026
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/eei.v15i2.11306

Abstract

Low-dose computed tomography (LDCT) reduces radiation exposure but introduces elevated noise and streak artifacts that degrade structural fidelity. This paper proposes a graph-based LDCT denoising framework that stabilizes graph construction through explicit vertex and edge labelling guided by paired full-dose CT (FDCT) data. The overlapping LDCT patches are modeled as vertices, and FD-guided affinities are used to build a structurally consistent adjacency matrix and a Laplacian spectrum that are less sensitive to noise. Denoising is performed by spectral filtering via spectral graph wavelet transform (SGWT), followed by overlap–add patch aggregation for image reconstruction. Experiments on paired LDCT/FDCT slices (318 pairs) show that FD-guided labelling improves denoising quality compared with conventional filters and non-guided graph baselines. Quantitative results demonstrate higher peak signal-to-noise ratio (PSNR)/structural similarity index measure (SSIM) with improved edge and feature preservation, indicating better structural boundary retention under noise suppression.
Co-Authors Fajri, Muhammad Rafif Haryeni, Debi Oktia Hilda Assiyatun, Hilda Iwan Setiawan Maulidyani Abu Rina Ratianingsih Rosiyadi, Didi Saputro, Suhadi Wido Zulfaneti Zulfaneti