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].

The study of such graphs is called graph theory. Engineers need to find planarity in a graph when, for example, they are designing a computer chip without a crossed wire.

These mathematical phenomena appear in everything from entanglement interactions in quantum mechanics to the trajectory of a disease spreading through a population. If a pharmacologist wanted to model ...

Mathematicians have long sought to develop algorithms that can compare any two graphs. In practice, many algorithms always seem to work efficiently. But in theory, there is no guarantee.