Changes between Initial Version and Version 1 of Ticket #16370, comment 21


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Timestamp:
06/04/14 09:07:02 (7 years ago)
Author:
knsam
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  • Ticket #16370, comment 21

    initial v1  
    55- Adjacency graph: the points are the vertices; two vertices are adjacent if they are incident in a common line.
    66
    7 - Block Intersection graph: the vertices are blocks of the system and two vertices are adjacent if they meet in some number of points.
     7- Block Intersection graph: the vertices are lines of the system and two vertices are adjacent if they meet in some fixed condition on the number of points.
    88
    99As I indicated above, it is common to call the graphs that we are talking about as Block intersection graphs.
    1010
    11 A quasi-symmetric design is a 2-design with atmost two block intersection numbers. Those with only one block intersection number are the square (or symmetric) 2-designs. One can solve the equations one obtains by using Fischer's variance counting to get the parameters in this case.
     11A quasi-symmetric design is a 2-design with atmost two block intersection numbers. Those q.s designs with only one block intersection number are the square (or symmetric) 2-designs. One can solve the equations one obtains by using Fischer's variance counting to get the parameters of the SRG in this case.
    1212
    1313Curiously, petersen graph is the block intersection graph of the 2-design 2-(6, 3, 2) (this is a quasi-symmetric design: any two blocks meet in 0 points or 1 point) where you define adjacency among blocks as "being disjoint". See [http://sina.sharif.edu/~emahmood/papers/MR1147979.PDF here].