Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

Semigroups of transformations and endomorphisms have emerged as powerful algebraic frameworks to elucidate the underlying structures of graphs. By harnessing the principles of semigroup theory, ...

At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student. The proof joined a long list of mathematical results that Sah, who turned 21 ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...

Back in the hazy olden days of the pre-2000s, navigating between two locations generally required someone to whip out a paper map and painstakingly figure out the most optimal route between those ...