The Maximum Order of Adjacency Matrices with a Given Rank
نویسندگان
چکیده
منابع مشابه
The maximum order of reduced square (0,1)-matrices with a given rank
The maximum order of a square (0, 1)-matrix A with a fixed rank r is considered, provided A has no repeated rows or columns. When A is the adjacency matrix of a graph, Kotlov and Lovász [A. Kotlov and L. Lovász. The rank and size of graphs. J. Graph Theory, 23:185–189, 1996.] proved that the maximum order equals Θ(2r/2). In this note, it is showed that this result remains correct if A is symmet...
متن کاملEla the Maximum Order of Reduced Square (0, 1)-matrices with a given Rank∗
The maximum order of a square (0, 1)-matrix A with a fixed rank r is considered, provided A has no repeated rows or columns. When A is the adjacency matrix of a graph, Kotlov and Lovász [A. Kotlov and L. Lovász. The rank and size of graphs. J. Graph Theory, 23:185–189, 1996.] proved that the maximum order equals Θ(2r/2). In this note, it is showed that this result remains correct if A is symmet...
متن کاملMaximum Order of Triangle-Free Graphs with a Given Rank
The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle-free graphs with a given rank and characterize all such graphs achieving the maximum order.
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We show that the maximum rank of block lower triangular Toeplitz block matrices equals their term rank if the blocks fulfill a structural condition, i.e., only the locations but not the values of their nonzeros are fixed.
متن کاملOn the maximum rank of Toeplitz block matrices of blocks of a given pattern
We show that the maximum rank of block lower triangular Toeplitz block matrices equals their term rank if the blocks fulfill a structural condition, i.e., only the locations but not the values of their nonzeros are fixed.
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2010
ISSN: 1556-5068
DOI: 10.2139/ssrn.1706570