Edge rotations and distance between graphs
For a nontrivial connected graph , the -degree of a vertex in a graph is the number of copies of in containing . A graph is -continuous (or -degree continuous) if the -degrees of every two adjacent vertices of differ by at most 1. All -continuous graphs are determined. It is observed that if is a nontrivial connected graph that is -continuous for all nontrivial connected graphs , then either is regular or is a path. In the case of a 2-connected graph , however, there...
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