Abstract:Abstract. Using number theoretical tools, we prove two main results for random r-regular circulant graphs with n vertices, when n is sufficiently large and r is fixed. First, for any fixed ε > 0, prime n and L ≥ n 1/r (log n) 1+1/r+ε , walks of length at most L terminate at every vertex with asymptotically the same probability. Second, for any n, there is a polynomial time algorithm to find a vertex bisector and an edge bisector, both of size less than n 1−1/r+o(1) . As circulant graphs are popular network top… Show more
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