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 ...

D. Fan, S. Goryainov, X. Huang, H. Lin, The spanning k-trees, perfect matchings and spectral radius of graphs, Linear Multilinear Algebra 70 (2022), 7264–7275. P ...

We call a rational map f graph critical if any critical point either belongs to an invariant finite graph G, or has minimal limit set, or is nonrecurrent and has limit set disjoint from G. We prove ...

Power graphs provide an innovative way to visualise and analyse the algebraic structure of finite groups. In a power graph, the elements of a finite group serve as vertices, and an edge is drawn ...

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 ...

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon. When you walk into a room full of people, you can ...

In 2008, the mathematician Oded Schramm died in a hiking accident in the Cascade mountains some 50 miles east of Seattle. Though he was just 46 years old, he had constructed entirely new areas of ...

At a time when every enterprise looks to leverage generative artificial intelligence, data sites are turning their attention to graph databases and knowledge graphs. The global graph database market ...