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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal Focus Action of Research Mathematic (Factor M) Journal of Applied Statistics, Mathematics, and Data Science
Dliou, Kamal
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Computer Science & IT Decision Sciences, Operations Research & Management Education Mathematics Other

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On the RACN of the comb product of the cycle C_3 with path P_n and broom Br_(n,m) Septory, Brian Juned; Retnowardani, Dwi Agustin; Dliou, Kamal
Journal Focus Action of Research Mathematic (Factor M) Vol. 8 No. 1 (2025): Vol. 8 No. 1 (2025)
Publisher : Universitas Islam Negeri (UIN) Syekh Wasil Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30762/f_m.v8i1.4755

Abstract

The combination of rainbow coloring and anti-magic labeling is known as Rainbow Antimagic Coloring (RAC). The Rainbow Antimagic Connection Number (RACN) of a graph G is the smallest number of colors induced by all edge weights under an antimagic labeling, symbolized as rac(G) A graph is said to have rainbow antimagic connectivity if for every pir of vetices x∈V(G), there exits a rainbow antimagic path, wherin all edge weights along the path are distinct. Let G be a graph with vertex set V(G) and edge set E(G). A bijective function f from V(G) to {1,2,…,|V(G)|} is applied, wherein the weight of the edge uv∈E(G) is defined as w(uv) under f which is obtained from w(xv)=f(x)+f(v). A rainbow path x-v is a path in a vertex-labeled graph G if for any two edges xv,x' v'∈E(P) the path satisfies w(xv)≠w(x'v'). If there is a rainbow x-v path P for every two vertices x,v∈V(G) then the function f is called a rainbow antimagic labeling of G. A graph G we say has an RAC, if we assign each edge xv with an edge weight color w(xv). In this paper, we present the RACN of the comb product of cycle C_3 with path P_n and broom Br_(n,m) symbolized by C_3⊳ P_n and C_3⊳Br_(n,m). A comb operation on a graph G, symbolized as G⊳H, is a graph product wherein each vertex of G is replaced by a copy of H, maintaining the structure of G. This operation helps construct new classes of graphs with specific connectivity and labeling properties.
BILANGAN DOMINASI TOTAL PADA GRAF HASIL OPERASI KORONA SISI DARI GRAF LINTASAN DAN SEBARANG GRAF Retnowardani, Dwi Agustin; Dliou, Kamal; Wulandari, Audia Dwi Retno
ESTIMATOR : Journal of Applied Statistics, Mathematics, and Data Science Vol. 1 No. 2 (2023)
Publisher : Program Studi Statistika Universitas PGRI Argopuro Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31537/estimator.v1i2.1534

Abstract

Misalkan adalah graf terhubung dan tidak memiliki arah. Himpunan dari titik-titik di graf adalah himpunan dominasi dari jika setiap titik di terdominasi oleh paling sedikit satu titik . Kardinalitas minimal dari himpunan dominasi di disebut bilangan dominasi dan disimbolkan dengan . Untuk suatu graf terhubung , suatu himpunan dari titik-titik di adalah himpunan dominasi total dari jika setiap titik di terhubung langsung ke suatu titik di . Anggota himpunan dominasi total harus terhubung langsung dengan titik lain di . Kardinalitas minimal dari himpunan dominasi total di disebut bilangan dominasi total dan disimbolkan dengan . Operasi korona sisi dari dua graf yang dinotasikan dengan dari graf dan dide?nisikan sebagai graf yang diperoleh dengan mengambil satu buah duplikat dari graf dan duplikat sebanyak sisi pada graf , dan kemudian menghubungkan dua titik ujung dari sisi ke- pada dengan setiap titik duplikat ke- pada .
Analysis of Resolving Efficient Dominating Set and Its Application Scheme in Multi-Step Time Series Forecasting of pH and Soil Moisture in Horizontal Farming Dliou, Kamal; Aziza, Adinda Putri; Dafik, Dafik; Kristiana, Arika Indah; Retnowardani, Dwi Agustin
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.29960

Abstract

This research focuses on the analyzing the Resolving Efficient Dominating Set (REDS) and its application scheme in horizontal farming using the Spatial Temporal Graph Neural Network (STGNN). Soil moisture and pH are crucial factors that affect the growth and yield, as they directly impact productivity and plant health. In cases where soil moisture and pH are lacking, various types of companion planting need to be watered. In such planting systems, a central role is needed to monitor soil moisture and pH levels effectively. The placement of operators in this system requires the application of mathematical concepts, specifically graph theory. In this study, we explore graph theory, particularly the Resolving Efficient Dominating Set. This involves ensuring that each vertex  is dominated by exactly one vertex in D, with no adjacent with another vertex, and the representation of vertex  concerning  is not the same. To effectively address this issue, including soil moisture and pH data, is required to predict future soil moisture and pH values in companion farming. Spatial Temporal Graph Neural Network (STGNN) technique proves to be useful in solving the problem of soil moisture and pH by understanding and modeling multi-step time series data. This technique aids in effectively managing and optimizing horizontal farming.
Co-Authors Arika Indah Kristiana Aziza, Adinda Putri D. Dafik Dwi Agustin Retnowardani Septory, Brian Juned Wulandari, Audia Dwi Retno