Abstract
The factorization of an element x from a numerical monoid can be represented visually as an irreducible divisor graph G.x/. The vertices of G.x/ are the monoid generators that appear in some representation of x, with two vertices adjacent if they both appear in the same representation. In this paper, we determine precisely when irreducible divisor graphs of elements in monoids of the form NDhn; nC 1;:::; nC ti where 0 t < n are complete, connected, or have a maximum number of vertices. Finally, we give examples of irreducible divisor graphs that are isomorphic to each of the 31 mutually nonisomorphic connected graphs on at most five vertices.
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