Surface-links with square-type ch-graphs

Amorphic association schemes with negative Latin square-type graphs

Applying results from partial difference sets, quadratic forms, and recent results of Brouwer and Van Dam, we construct the first known amorphic association scheme with negative Latin square type graphs and whose underlying set is a nonelementary abelian 2-group. We give a simple proof of a result of Hamilton that generalizes Brouwer’s result. We use multiple distinct quadratic forms to constru...

Random Latin square graphs

In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and seve...

Square contractions of graphs

Square-free perfect graphs

Links associated with generic immersions of graphs

As an extension of the class of algebraic links, A’Campo, Gibson, and Ishikawa constructed links associated to immersed arcs and trees in a two-dimensional disk. By extending their arguments, we construct links associated to immersed graphs in a disk, and show that such links are quasipositive. AMS Classification 57M25; 57M27