Zhanhe Zhang

Regular Graphs with Pairwise Distinct K_t-Degrees

For a fixed integer \(t \ge 3\), let \(\kappa_t(v)\) denote the number of copies of \(K_t\) containing a vertex \(v\). We prove that for every \(t \ge 6\) and every sufficiently large even integer \(r\), there exists an explicit connected \(r\)-regular graph on \(2r+2\) vertices...

Core Label Orders of the Lattices W(m,n)

We determine the core label orders of the lattices W(m,n). Although these orders cease to be join-semilattices when m ≥ 2 and n > 0, every interval admits an explicit product decomposition into a Boolean lattice and one-letter shuffle lattices. The decomposition follows from a te...

Core Label Orders of the Lattices W(m,n)

We determine the core label orders of the lattices W(m,n). Although these orders cease to be join-semilattices when m ≥ 2 and n > 0, every interval admits an explicit product decomposition into a Boolean lattice and one-letter shuffle lattices. The decomposition follows from a te...