This paper proves non-existence of nontrivial t-edge-balanced graphs for t >= 4 and computationally discovers the first examples for t = 3 after establishing necessary conditions on n and k.
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On $t$-edge-balanced graphs
This paper proves non-existence of nontrivial t-edge-balanced graphs for t >= 4 and computationally discovers the first examples for t = 3 after establishing necessary conditions on n and k.