Minimum rank and zero forcing number for butterfly networks

نویسندگان

  • Daniela Ferrero
  • Cyriac Grigorious
  • Thomas Kalinowski
  • Joseph F. Ryan
  • Sudeep Stephen
چکیده

The minimum rank of a simple graph G is the smallest possible rank over all symmetric real matrices A whose nonzero off-diagonal entries correspond to the edges of G. Using the zero forcing number, we prove that the minimum rank of the r-th butterfly network is 1 9 [ (3r + 1)2r+1 − 2(−1)r ] and that this is equal to the rank of its adjacency matrix.

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عنوان ژورنال:
  • CoRR

دوره abs/1607.07522  شماره 

صفحات  -

تاریخ انتشار 2016