On Topologies on Simple Graphs and Their Applications in Radar Chart Methods

This paper introduces a novel topology (upper approximated G-topology) on vertex sets of graphs using rough upper approximation neighborhoods, extending prior work on graph-induced topologies. Key results include characterizing discrete/indiscrete topologies for complete graphs, cycle graphs, and bipartite graphs (Theorems 1–3). The discrete topology for cycle graphs Cn, n>5, is particularly insightful. Exploring further, we delve into the continuity and isomorphism of graph mappings. Subsequently, we apply these findings to enhance radar chart graphical methods through the analysis of corresponding graph structures. These applications demonstrate practical relevance, linking graph structures to data visualization.