Graph theory may show how individuals are connected, for example, but not capture the ways in which clusters of friends on social media influence each other’s behavior.

Additionally, research on planar graphs has yielded new insights into the anti-Ramsey numbers for paths and cycles, thereby bridging classical graph theory with geometric constraints [3].

Commuting graphs have emerged as a powerful framework for elucidating complex relationships within finite group theory. In these graphs, vertices typically represent non-central elements of a ...