Results 1 to 10 of about 13,009 (241)
Maximum nullity and zero forcing of circulant graphs [PDF]
Special Matrices, 2020 The zero forcing number of a graph has been applied to communication complexity, electrical power grid monitoring, and some inverse eigenvalue problems.
Duong Linh +4 more
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Families of graphs with maximum nullity equal to zero forcing number
Special Matrices, 2018 The maximum nullity of a simple graph G, denoted M(G), is the largest possible nullity over all symmetric real matrices whose ijth entry is nonzero exactly when fi, jg is an edge in G for i =6 j, and the iith entry is any real number.
Alameda Joseph S. +7 more
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Maximum nullity of some Cayley graphs [PDF]
Cogent Mathematics & Statistics, 2018 Recently, the nullity, the algebraic multiplicity of the number zero in the spectrum of the adjacency matrix, of a molecular graph has received a lot of attention as it has a number of direct appli...
Ebrahim Vatandoost +1 more
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Signed graphs with maximum nullity two
Linear Algebra and its Applications, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marina Arav +2 more
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Positive semidefinite maximum nullity and zero forcing number
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.
Travis Peters
+6 more sources
Maximum nullity of Cayley graph [PDF]
, 2017 One of the most interesting problems on maximum nullity (minimum rank) is to characterize $M(\mathcal{G})$ ($mr(\mathcal{G})$) for a graph $\mathcal{G}$. In this regard, many researchers have been trying to find an upper or lower bound for the maximum nullity. For more results on this topic, see \cite{4}, \cite{2}, \cite{10} and \cite{1}. In this paper,
Ebrahim Vatandoost +1 more
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Compatible Forts and Maximum Nullity of a Graph [PDF]
Graphs and CombinatoricsWe consider bounds on maximum nullity of a graph via transversal numbers of compatible collections of forts. Results include generalizations of theorems from symmetric to combinatorially symmetric matrices, special bases of matrix nullspaces derived from transversal sets, and examples of issues that arise when considering only minimal forts and how to ...
Veronika Furst +3 more
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The number of P-vertices in a matrix with maximum nullity [PDF]
Linear Algebra and its Applications, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rosário Fernandes, Henrique F. da Cruz
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Maximum Nullity and Forcing Number on Graphs with Maximum Degree at most Three [PDF]
, 2019 A dynamic coloring of the vertices of a graph $G$ starts with an initial subset $F$ of colored vertices, with all remaining vertices being non-colored. At each time step, a colored vertex with exactly one non-colored neighbor forces this non-colored neighbor to be colored.
Meysam Alishahi +2 more
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Maximum and minimum nullity of a tree degree sequence [PDF]
, 2018 The nullity of a graph is the multiplicity of the eigenvalue zero in its adjacency spectrum. In this paper, we give a closed formula for the minimum and maximum nullity among trees with the same degree sequence, using the notion of matching number and annihilation number.
Gonzalo Molina, Daniel A. Jaume
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