Abstract: We generalize the definition of an antiregular graph by
subjecting antiregularity to the presence of a given set P
of graph properties. In this paper, we study the cases where P
=
andP
=
{vertex-connectivity, thresholdness}. We discuss the construction of these
classes, looking also for structural characteristics and some properties such as
hamiltonicity and tree-universality.
Keywords and phrases: antiregularity, connectivity, threshold graphs, tree-universality.
