The picture above shows our game represented as a graph — a collection of points (called vertices) and segments between them (called edges). The dilemma you face exemplifies a simple but profound idea ...

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.

Mathematicians have long sought to develop algorithms that can compare any two graphs. In practice, many ...

Cayley graphs provide a powerful and intuitive framework linking group theory with graph theory by representing groups through vertices and edges defined by a generating set. In the realm of ...