Regular Graph

Regular graphs, characterized by each vertex having the same degree, are a fundamental structure in graph theory with applications across diverse fields. Current research focuses on developing efficient algorithms for distinguishing and analyzing these graphs, employing techniques such as Group Equivariant Non-Expansive Operators (GENEOs) and dual basis approaches within multidimensional scaling. These investigations are driven by the need for improved methods in areas like machine learning (graph classification) and the study of social network dynamics (e.g., voting models on regular graphs), highlighting the importance of understanding regular graph properties for both theoretical and practical advancements.