On realization graphs of degree sequences
Copyright policy )On realization graphs of degree sequences
Given the degree sequence $d$ of a graph, the realization graph of $d$ is the graph having as its vertices the labeled realizations of $d$, with two vertices adjacent if one realization may be obtained from the other via an edge-switching operation. We describe a connection between Cartesian products in realization graphs and the canonical decomposition of degree sequences described by R.I. Tyshkevich and others. As applications, we characterize the degree sequences whose realization graphs are triangle-free graphs or hypercubes.
10 pages, 5 figures
- University of Rhode Island United States
- Department of Mathematics
degree sequence, canonical decomposition, Graph operations (line graphs, products, etc.), Vertex degrees, realization graph, 510, 004, FOS: Mathematics, 05C07, Mathematics - Combinatorics, Combinatorics (math.CO)
degree sequence, canonical decomposition, Graph operations (line graphs, products, etc.), Vertex degrees, realization graph, 510, 004, FOS: Mathematics, 05C07, Mathematics - Combinatorics, Combinatorics (math.CO)
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