The spectral characteristics of graphs and matrices form a central pillar of modern mathematical physics and network theory. At its core, the adjacency matrix of a graph encodes connectivity by ...
Cayley graphs provide a natural bridge between algebra and combinatorics by encoding a group and a generating set as vertices and edges, respectively. The eigenvalues of their adjacency and Laplacian ...
In 1950 Edward Nelson, then a student at the University of Chicago, asked the kind of deceptively simple question that can give mathematicians fits for decades. Imagine, he said, a graph — a ...