This is a survey paper on the second largest eigenvalue λ₂ of the adjacency matrix of a graph. Among the topics presented are the graphs with small λ₂, bounds for λ₂, algebraic connectivity, graphs ...

Abstractions blog A New Algorithm for Graph Crossings, Hiding in Plain Sight Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory ...

Abstract. In the present paper we are interested in the study of the distance Laplacian eigenvalues of a connected graph with fixed order n and chromatic number χ. We prove lower bounds on the ...

DeepMind breaks 50-year math record using AI; new record falls a week later AlphaTensor discovers better algorithms for matrix math, inspiring another improvement from afar.