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, ...

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory. This past October, as Jacob Holm and Eva Rotenberg were thumbing through a ...

In algorithms, as in life, negativity can be a drag. Consider the problem of finding the shortest path between two points on a graph — a network of nodes connected by links, or edges. Often, these ...

Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a ...

Researchers thought that they were five years away from solving a math riddle from the 1980's. In reality, and without knowing, they had nearly cracked the problem and had just given away much of the ...

Energy diagram illustrating the dependence of eigenstate energies on quasiperiodic potential strength. Red dashed lines show the existence of two mobility edges in the system. In quantum systems, ...