Advanced Mathematical Models & Applications

This study introduces an innovative approach to river erosion prediction by integrating the concept of Strong Rainbow Antimagic Coloring (SRAC) with the Spatial Temporal Graph Neural Network (STGNN) model. SRAC, an advanced graph theory concept, assigns unique edge colors to graph structures, ensuring distinct shortest paths. This property is leveraged to represent river networks and analyze physical characteristics such as discharge, depth, and width, which are critical indicators of erosion. The STGNN model is then employed to process both spatial and temporal data, enabling accurate prediction of erosion patterns. The main objectives of this research are: to determine the lower bound of SRAC; determine SRAC of book, triangular book, and ladder graphs; and implement of SRAC concept in river erosion analysis using STGNN model. Results demonstrate that the combination of SRAC and STGNN effectively identifies high-risk erosion areas and provides actionable insights for sustainable river management and environmental conservation. This study contributes to hydrological research by offering a graph-based predictive framework with potential applications in water resource management and disaster mitigation.