Minimum rank, maximum nullity, and zero forcing number of simple digraphs
نویسندگان
چکیده
منابع مشابه
Ela Minimum Rank, Maximum Nullity, and Zero Forcing Number of Simple Digraphs
A simple digraph describes the off-diagonal zero-nonzero pattern of a family of (not necessarily symmetric) matrices. Minimum rank of a simple digraph is the minimum rank of this family of matrices; maximum nullity is defined analogously. The simple digraph zero forcing number is an upper bound for maximum nullity. Cut-vertex reduction formulas for minimum rank and zero forcing number for simpl...
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Combinatorial matrix theory, which involves connections between linear algebra, graph theory, and combinatorics, is a vital area and dynamic area of research, with applications to fields such as biology, chemistry, economics, and computer engineering. One area generating considerable interest recently is the study of the minimum rank of matrices associated with graphs. Let F be any field. For a...
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The zero forcing number Z(G) is used to study the minimum rank/maximum nullity of the family of symmetric matrices described by a simple, undirected graph G. The positive semidefinite zero forcing number is a variant of the (standard) zero forcing number, which uses the same definition except with a different color-change rule. The positive semidefinite maximum nullity and zero forcing number f...
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The zero forcing number Z(G) is used to study the minimum rank/maximum nullity of the family of symmetric matrices described by a simple, undirected graph G. The positive semidefinite zero forcing number is a variant of the (standard) zero forcing number, which uses the same definition except with a different color-change rule. The positive semidefinite maximum nullity and zero forcing number f...
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The minimum rank of a simple graph G is the smallest possible rank over all symmetric real matrices A whose nonzero off-diagonal entries correspond to the edges of G. Using the zero forcing number, we prove that the minimum rank of the r-th butterfly network is 1 9 [ (3r + 1)2r+1 − 2(−1)r ] and that this is equal to the rank of its adjacency matrix.
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2013
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1686