Application of Rainbow Vertex Antimagic Coloring in Multi-Step Time Series Forecasting for Efficient Railway Passenger Load Management
Keywords:
Rainbow Vertex Antimagic Coloring, Time Series Forecasting, Spatial Temporal Graph Neural Networks, Railway Station Passengers Load
Abstract
Let $G$ be a simple graph and connected. If there is a bijection function $f:E(G)\to\{1,2,\cdots,|E(G)|\}$ and the rainbow vertex antimagic coloring is under the condition all internal vertices of a path $x-y$ for any two vertices $x$ and $y$ have different weight $w(x)$, where $w(x) = \Sigma_{xx' \in E(G)}f(xx')$. The least number of colors used among all rainbow colorings produced by rainbow vertex antimagic labelings of a graph $G$ is the rainbow vertex antimagic connection number, $rvac(G)$. Our goal in this study is to prove some theorems related to $rvac(G)$. Furthermore, we apply RVAC as an administrative operator that controls passenger load anomalies at stations. This control uses spatio temporal multivariate time series Graph Neural Network (GNN) forecasting. Based on the results, we found that the metric evaluation of our GNN outperformed other models such as HA, ARIMA, SVR, GCN and GRU.References
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\bibitem{Li}Li, X. \& Shi, Y., "On the Rainbow Vertex-Connection", \textit{Discussiones Mathematicae Graph Theory}, \textbf{33}(2), pp. 307-313, 2013.
\bibitem{Simamora} Simamora, D. N. S.\& Salman, A. N. M., "The Rainbow (Vertex) Connection Number of Pencil Graphs", \textit{Procedia Computer Science}, \textbf{74}, pp. 138-142, 2015.
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\bibitem{Dafik} Dafik, F. Susanto, R. Alfarisi, B.J. Septory, I.H. Agustin, M. Venkatachalam, "On Rainbow Antimagic Coloring of Graphs", \textit{Advanced Mathematical Models \& Applications}, (2021), \textbf{6}, pp. 278-291.
\bibitem{Kamila} Kamila, A. A. U., Dafik, Kristiana, A. I., Nisviasari, R., and. Kurniawati, E. Y. 2023. "On Rainbow Vertex Antimagic Coloring of Shell Related Graphs". ICCGANT 2022. Advances in Physics Research by Atlantis Press, Vol. 6, pp. 17-29.
\bibitem{Mursyidah} Mursyidah, I. L., Kristiana, A. I., Agustin, I. H., Maylisa, I. N., and Alfarisi, R. 2023. "On Rainbow Antimagic Coloring of Some Classes of Graphs". ICCGANT 2022. Advances in Physics Research by Atlantis Press, Vol. 6, pp. 73-93.
\bibitem{Marsidi1} Marsidi, Agustin, I. H., Dafik, and Kurniawati, E. Y. 2021. "On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion". CAUCHY: Jurnal Matematika Murni dan Aplikasi. Vol. 7, pp. 64-72.
\bibitem{Marsidi2} Marsidi, Agustin, I. H., Dafik, Kurniawati, E. Y., and Nisviasari, R. 2022. "The Rainbow Vertex Antimagic Coloring of Tree Graphs". Journal of Physics: Conference Series. 2157 (2022) 012019.
\bibitem{Febrinanto1} F. G. Febrinanto, F. Xia, K. Moore, C. Thapa, and C. Agarwal. Graph Lifelong Learning: A Survey, IEEE Computational Intelligent Magazine (2020), pp. 1-19.
\bibitem{Febrinanto2} F. G. Febrinanto, F. Xia, K. Moore, C. Thapa, C. Agarwal, and T. J. Watson. Graph Lifelong Learning: A Survey. EEE COMPUTATIONAL INTELLIGENCE MAGAZINE, VOL. 00, NO. 0, 2022.
\bibitem{STGNN} I. H. Agustin, B. Arianti, DAFIK, M. FATEKUROHMAN, and R. I. Baihaki, "Application of Spatial Temporal Graph Neural Network in Analyzing the Distribution of Goods Shipping with Dominating Set Technique". El-Cezeri, 11(1), 10-22.
\bibitem{Zhao} Zhao, L., Song, Y., Zhang, C., Liu, Y., Wang, P., Lin, T., Deng, M., and Li, Haifeng. 2015. “T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction”. arXiv:1811.05320v3.
\bibitem{Bai2} Bai. J., Zhu, J., Song, Y., Zhao, L., Hou, Z., Du, R., and Li, H. 2021. “A3T-GCN: Attention Temporal Graph Convolutional Network for Traffic Forecasting”. International Journal of Geo-Information. Vol. 10, No. 485, page 1-16.
\bibitem{Zhang} Zhang, C., Zhou, H. Y., Qiu, Q., Jian, Z., Zhu, D., Cheng, C., He, L., Liu, G., Wen, X., and Hu, R. 2022. “Augmented Multi-Component Recurrent Graph Convolutional Network for Traffic Flow Forecasting”. International Journal of Geo-Information. Vol. 11, No. 88, page 1-17.
\bibitem{Lv} Lv, M., Hong, Z., Chen, L., Chen, T., Zhu, T., and Ji, S. 2020. “Temporal Multi-Graph Convolutional Network for Traffic Flow Prediction”. IEEE Transactions on Intelligent Transportation Systems. Page 1-12.
\bibitem{Wang} Wang, Y., Qin, Y., Guo, J., Cao, Z., and Jia, L. 2022. “Multi-Point Short-Term Prediction of Station Passenger Flow based on Temporal Multi-Graph Convolutional Network”. Physica A: Statistical Mechanics and Its Applications”. Vol. 604, No. 15, page 1-15.
\bibitem{Tang} Tang, J., Liang, J., Liu, F., Hao, J., and Wang, Y. 2021. “Multi-Community Passenger Demand Prediction at Region Level based on Spatio-Temporal Graph Convolutional Network”. Transporation Research Part C: Emerging Technologies. Vol. 124, page 1-12.
Published
2025-05-06
How to Cite
Dafik, Kurniawati, E. Y., Agustin, I. H., Kristiana, A. I., Adawiyah, R., & Venkatachalam, M. (2025). Application of Rainbow Vertex Antimagic Coloring in Multi-Step Time Series Forecasting for Efficient Railway Passenger Load Management. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2214
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Section
Research Articles
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