Results 11 to 20 of about 2,050,476 (233)
Maximum generic nullity of a graph [PDF]
Linear Algebra and its Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hogben, Leslie, Shader, Bryan
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Change of nullity of a graph under two operations [PDF]
Kuwait Journal of Science, 2021 Two adjacent or non-adjacent vertices of a graph G are said to be identified, if they are combined to form one vertex whose neighbor is the union of their neighborhoods (ignoring any loops or multiple edges formed).
Gohdar H. Mohiaddin, Khidir R. Sharaf
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On the nullity number of graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2017 The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007) 60--67] that $\eta \le n - D$, where $\eta$, n and D denote the nullity number, the order ...
Mustapha Aouchiche, Pierre Hansen
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Minimum rank, maximum nullity and zero forcing number for selected graph families [PDF]
Involve, a Journal of Mathematics, 2010 The minimum rank of a simple graph G is dened to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i 6 j) is nonzero whenever fi;jg is an edge in G and is zero otherwise. Maximum nullity is taken over the same set of matrices, and the sum of maximum nullity and minimum rank is the order of the graph.
Almodovar, Edgard +6 more
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Techniques for determining equality of the maximum nullity and the zero forcing number of a graph
The Electronic Journal of Linear Algebra, 2021 It is known that the zero forcing number of a graph is an upper bound for the maximum nullity of the graph (see [AIM Minimum Rank - Special Graphs Work Group (F. Barioli, W. Barrett, S. Butler, S. Cioab$\breve{\text{a}}$, D. Cvetkovi$\acute{\text{c}}$, S. Fallat, C. Godsil, W. Haemers, L. Hogben, R. Mikkelson, S. Narayan, O. Pryporova, I.
Young, Derek
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A note on minimum rank and maximum nullity of sign patterns [PDF]
The Electronic Journal of Linear Algebra, 2011 The minimum rank of a sign pattern matrix is defined to be the smallest possible rank over all real matrices having the given sign pattern. The maximum nullity of a sign pattern is the largest possible nullity over the same set of matrices, and is equal to the number of columns minus the minimum rank of the sign pattern.
Hogben, Leslie
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Minimum rank, maximum nullity, and zero forcing number of simple digraphs [PDF]
The Electronic Journal of Linear Algebra, 2013 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.
Berliner, Adam +5 more
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Positive semidefinite maximum nullity and zero forcing number [PDF]
The Electronic Journal of Linear Algebra, 2012 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 semidef- inite zero forcing number is a variant of the (standard) zero forcing number, which uses the same definition except with a different color-change rule.
Peters, Travis
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Tree Cover Number and Maximum Semidefinite Nullity of Some Graph Classes
The Electronic Journal of Linear Algebra, 2020 Let $G$ be a graph with a vertex set $V$ and an edge set $E$ consisting of unordered pairs of vertices. The tree cover number of $G$, denoted $\tau(G)$, is the minimum number of vertex disjoint simple trees occurring as induced subgraphs of $G$ that cover all the vertices of $G$.
Rachel Domagalski, Sivaram Narayan
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Maximum nullity of outerplanar graphs and the path cover number [PDF]
Linear Algebra and its Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sinkovic, J.H., Sinkovic, John
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