Create a collection of ten distinct
subsets of S = {1, 2, 3, 4, 5, 6} such that:
1. each subset contains three elements,
2. each element of S appears in five subsets, and
3. each pair of elements from S appears in exactly
two subsets.
Please explain how you did it.
{1, 2, 3}, {1, 2, 4}, {1, 3, 5}, {1, 4, 6}, {1, 5, 6}, {2, 3, 6}, {2, 4, 5}, {2, 5, 6}, {3, 4, 5}, {3, 4, 6}
The interesting thing is that every two subsets have at least one number in common. If you connect the subsets that have two numbers in common, then you get the Petersen graph.
123
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124-245-+--+-345-135
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146------------------156
Edited on January 17, 2018, 10:36 am
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Posted by Math Man
on 2018-01-17 08:19:50 |
Solution
