The field of graph theory has been around since 1736, when Leonhard Euler published an article on the subject of the Seven Bridges of Königsberg (in Prussia, today’s Kaliningrad in Russia).

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 ...

In theory, it cannot be ruled out that the algorithms might run for longer than the age of the universe. But in practice, many algorithms seem to work just fine.

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].