On b-Coloring Analysis of Graphs: An Application to Spatial-Temporal Graph Neural Networks for Multi-Step Time Series Forecasting of Soil Moisture and pH in Companion Farming

Authors

  • Arika Indah Kristiana Universitas Jember
  • Elisa Rachmasari
  • Dafik .
  • Ika Hesti Agustin
  • Indah Lutfiyatul Mursyidah PUI-PT Combinatorics and Graph, CGANT-University of Jember, Jember
  • Ridho Alfarisi

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5409

Keywords:

bColoring, companion farming, multi-step time series forecasting

Abstract

Let G be a pair of two sets (V,E) with vertex set V and edge set E. A proper coloring of a graph G is a vertex coloring of it such that no two adjacent vertices in G have the same color. By bColoring, we define a coloring of the vertex of G such that each color class has at least one vertex that adjacent with all other color classes. The bchromatic number of graph G, denoted by φ(G), is the largest integer k such that  graph G has bColoring with k colors. In this paper, we will explore some new lemmas or theorems regarding to φ(G). Furthermore, to see the robust application of bColoring of graph, at the end of this paper we will illustrate the implementation of bColoring on spatial temporal graph neural networks (STGNN) multi-step time series forecasting on soil moisture and pH of companion farming.

Author Biography

  • Indah Lutfiyatul Mursyidah, PUI-PT Combinatorics and Graph, CGANT-University of Jember, Jember

    PUI-PT Combinatorics and Graph, CGANT-University of Jember, Jember, Indonesia

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Published

2024-10-31

Issue

Section

Nonlinear Analysis

How to Cite

On b-Coloring Analysis of Graphs: An Application to Spatial-Temporal Graph Neural Networks for Multi-Step Time Series Forecasting of Soil Moisture and pH in Companion Farming. (2024). European Journal of Pure and Applied Mathematics, 17(4), 3356-3369. https://doi.org/10.29020/nybg.ejpam.v17i4.5409