Coxeter theory investigates groups generated by reflections and the geometric structures arising from their actions, such as root systems and Dynkin diagrams. This body of work underpins vast areas of ...

A tree must be acyclic, meaning it should not contain any cycles. A cycle is a path that starts and ends at the same vertex ...

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 ...

For any integer 𝑘 ≥ 2, a graph 𝐺 is called 𝑘-leaf-connected if |V(G)|≥k+1 and given any subset 𝑆 ⊆ 𝑉(𝐺) with |S|=k,G always has a spanning tree 𝑇 such that 𝑆 is precisely the set of leaves of ...

All products featured on WIRED are independently selected by our editors. However, we may receive compensation from retailers and/or from purchases of products through these links. Learn more. Graph ...

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...

Graph neural networks (GNNs) have emerged as a powerful framework for analyzing and learning from structured data represented as graphs. GNNs operate directly on graphs, as opposed to conventional ...

For most of us, the word graph brings back memories (not always pleasant) of pencils and rulers and quadrille ruled paper, though a more recent generation may think instead of pie and bar charts ...