Graph distinguishing numbers constitute a vital parameter in understanding the symmetry properties of graphs. Fundamentally, the distinguishing number of a graph is the minimal number of labels ...

It is not known whether or not the stable rational cohomology groups H̃* (Aut(F∞); ℚ) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it ...

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 ...

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones. On January 8, three mathematicians posted a proof of a nearly 60-year-old problem in ...