[seqfan] closed walks in a complete graph
Brendan McKay
Brendan.McKay at anu.edu.au
Wed Aug 17 10:33:07 CEST 2022
Take a complete graph with n vertices and fix a starting vertex.
The number of closed walks of length k (i.e. k steps) from that vertex
to itself is (n-1)^(k-1), since we can walk arbitrarily for k-1 steps and
then return to the start on the k-th step.
How many closed walks of length k use exactly r distinct edges?
An example of a closed walk of length 4 using 2 distinct edges is u-v-w-v-u.
It must be known but I don't find it in OEIS.
Thanks, Brendan.
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