Parity Dimension for Graphs - A Linear Algebraic Approach

Authors: Amin A.T.1; Slater P.J.2; Zhang G-H.2

Source: Linear and Multilinear Algebra, Volume 50, Number 4, 1 January 2002 , pp. 327-342(16)

Publisher: Taylor and Francis Ltd

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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 2k for some value of k, and PD(G) = k. Using primarily linear algebraic techniques, we investigate the parity dimension of graphs.

Keywords: Parity dimension; Graphs; Linear algebra

Document Type: Research article

Affiliations: 1: Computer Science Department, University of Alabama in Huntsville, Huntsville, Alabama 35899, USA 2: Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, Alabama 35899, USA

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