Application of Rainbow Vertex Antimagic Coloring in Multi-Step Time Series Forecasting for Efficient Railway Passenger Load Management

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.