Abstract
For a graph G with closed neighborhood matrix N , the parity dimension of G , denoted PD( G ), is the dimension of the null space of N over the field ${\cal Z}_2$ . Equivalently, the number of vertex sets S in G with the property that S dominates each vertex an even number of times is 2 k for some value of k , and PD( G ) = k . Using primarily linear algebraic techniques, we investigate the parity dimension of graphs.
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