All Questions

A connected (and infinite) graph $U$ will be called $n$-universal if any connected graph with degree $\leqslant n$ admits an embedding in $U$. Is there a 3-universal graph with bounded degree?

As the title says, I'm interested in graphs with high girth and low diameter. Given a class $\Gamma$ of finite $k$-regular graphs, call a $\Gamma$-graph GD-extremal if every $\Gamma$-graph either has ...

When I search about expander graphs in google I see a lot of articles about expander Cayley graphs. Now my questions are as follows: Are all expander regular graphs are Cayley, or there is a special ...