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A sharp upper bound of the nullity of a connected graph in terms of order and maximum degree
Linear Algebra and its Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Zhi-Wen, Guo, Ji-Ming
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Electronic Journal of Linear AlgebraThis article studies the minimum rank of a (simple, undirected) graph, which is the minimum rank among all matrices in a space determined by the graph. It determines the exact set of graphs on eight vertices for which the nullity of a minimum rank matrix does not coincide with a bound determined by the zero forcing number of a graph.
John Hutchens, Wayne Barrett
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An upper bound for the nullity of a bipartite graph in terms of its maximum degree
Linear and Multilinear Algebra, 2015Let be a connected undirected graph without loops and multiple edges. The graph is said to be reduced if distinct vertices of have distinct neighbours in . The nullity of is the multiplicity of as an eigenvalue of the adjacency matrix of . By and , we respectively denote the order and the maximum degree of .
Ya-zhi Song +2 more
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Minimum-Rank and Maximum-Nullity of Graphs and Their Linear Preservers
Linear and Multilinear Algebra, 2022LeRoy B. Beasley, Seok-Zun Song
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The Number of P-Vertices for Acyclic Matrices of Maximum Nullity
Discrete Applied Mathematics, 2019Zhibin Du, Carlos M da Fonseca
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An Upper Bound for the Nullity of a Bipartite Graph in Terms of Its Maximum Degree
Linear and Multilinear Algebra, 2016Mingcui Zhang
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