  The degree sequence of a graph is a numerical method to characterize the
properties of graphs. Generalized forms of degree sequences exist for complete
graphs and complete graphs. Nikolopolus et al. characterized the number of
spanning trees from edge deletions and edge additions. Instead of investigating
the number of spanning trees of graphs that arise from edge additions and
deletions, we sought to characterize degree sequences of such graphs. We
conjecture a characterization for the degree sequence of the addition and edge
deletion for many families of graphs including threshold graphs and complete
multigraphs.
  Keywords: multigraphs, split graphs, degree sequence, threshold graph,
Havel-Hakimi, Ruch-Gutman, Edge Deletion
