Hadamard diagonalizable graphs of order at most 36

Jane Breen, Steve Butler, Melissa Fuentes, Bernard Lidický, Michael Philips, Alexander W. N. Riasanovsky, Sung-Yell Song, Ralihe R. Villagrán, Cedar Wiesman, Xiaohong Zhang

This page is containing computer assisted parts of the paper titled Hadamard diagonalizable graphs of order at most 36. A preliminary version of the paper can be downloaded here.

You can download the small technical things as one archive

• anc.zip (zip, around 1MB)

• Sage Math for running the sage program
• C++ compiler on MacOSX or Linux rebuilding the C++ version of the program
• nauty for rebuilding the C++ program

Description of the files

• all_hadamard.txt (3.3G) ... All $32 \times 32$ 13710027 Hadamard matrices
• all_of_them_unique.sorted.txt (847K) ... All 10196 Hadamard graphs on 32 vertices
• all_indexes.txt (1.2G) ... Each line corresponds to 13710027 Hadamard matrices from all_hadamard.txt and gives indexes to all_of_them_unique.sorted.txt.
• hadamard_commented.py ... Sage program for generating Hadamard Graphs bu Steve Butler
• hadamard_commented.cpp ... C++ version of the program above written by Bernard Lidicky
• hadamard_commented_column_test.cpp ... C++ version of the complete calculation including permuation of columns and support for the conjecture that permuting columns does not give new Hadamard graphs.
• hadamard_match.cpp ... Version of the calculation that creates all_indexes
• all_of_them_sage.sage ... all_of_them_unique.sorted.txt in a form that is easy to load to sage
• hadamard_explore.sage ... Example how to use all_of_them_sage.sage to study the graphs

File format

• all_hadamard.txt
  Each line contains one Hadamard matrix encoded as a string. For example, the first line is:
  FFFFFFFFFFFF0000CFC0FF00CF30C0FCAF0C38E3ACF0341F9AAAE29399A62E6CEC830BDAE86C8771E295A6A6E22B7C54E1CA61ADE136DA0BD9454C97D859726AD61C2B1DD4A99CA9D466B1C6D3921573BC1ACD26BA85D14DB64656B8B53167C1B361A93AB1D89AD48A731BA5891FB598874B864F85AD533684D7E87182FC4DCA
  Each letter corresponds to 4 entries in the matrix. Highest bit comes first and bit 1 corresponds to 1 in the matrix and 0 to -1 in the matrix. Notice the string has 256 characters and 256*4 = 1024 = 32 * 32.
• all_of_them_unique.sorted.tx
  Each line contains one graph on 32 vertices. For example line 3 is:
  _oCO?CA???_A????_?O????C??O?????C??A???????_??A???B???W??@_??B???B???@_???W???B?????
  It is in graph6 format, which is easy to load in programs such ase Sage.
• all_indexes.txt
  Each line corresponds to one matrix. The first line corresponds to the first line in all_hadamard.txt. Then the list of numbers correspond to lines in all_of_them_unique.sorted.tx. Example in the file all_indexes.txt the first line is
  0 30 53 8498 8506 8897 10021 10161 10191 10195
  This means that the first matrix produces Hadamard graphs on lines (0+1), (30+1), (53+1),.... in file all_of_them_unique.sorted.tx.