Abstract
A finite simple graph is uniformly (t, r)-regular if it has at least t vertices and the open neighbor set of each set of t of its vertices is of cardinality r. If t > 1, such a graph is trivially uniformly (t, r)-regular if either it is a matching (t = r) or r is the number of non-isolated vertices in the graph. We prove the result stated in the title.
Recommended Citation
McSorley, John P., Hoffman, Dean, Johnson, Peter, Lin, Kevin, Petrie, Caleb and Teirlinck, Luc. "There are no non-trivially uniformly (t,r)-regular graphs for t > 2.." Bulletin of the Institute of Combinatorics and its Applications 49 (Jan 2007): 11-14.
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