Hamiltonicity, diameter, domination, packing, and biclique partitions of Mycielski's graphs

Let omega(G), chi(G), A(G), bp(G), diam(G), eta(G), and gamma(G) be the clique number, chromatic number, adjacency matrix, biclique partition number, diameter, packing number, and domination number of a connected graph G. Mycielski constructed a graph mu(G) with omega(mu(G)) = omega(G) and chi(mu(G)) = chi(G)+1. We show: if G is Hamiltonian, then so is mu(G); if A(G) and A(G+nu) (G+nu is G joined with a vertex) are invertible, then so is A(mu(G)) and further bp(mu(G)) = \G\+1; eta(mu(G)) = eta(G); gamma(mu(G)) = gamma(G)+1; diam(mu(G)) = min(max(2, diam(G)), 4); and more. (C) 1998 Elsevier Science B.V. All rights reserved.