Results 1 to 10 of about 503 (213)
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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Zero forcing and maximum nullity for hypergraphs [PDF]
Discrete Applied Mathematics, 2020 The concept of zero forcing is extended from graphs to uniform hypergraphs in analogy with the way zero forcing was defined as an upper bound for the maximum nullity of the family of symmetric matrices whose nonzero pattern of entries is described by a given graph: A family of symmetric hypermatrices is associated with a uniform hypergraph and zeros ...
Leslie Hogben
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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...
E. Vatandoost, Y. Golkhandy Pour
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The Number of P-Vertices of Singular Acyclic Matrices: An Inverse Problem
Discussiones Mathematicae Graph Theory, 2020 Let A be a real symmetric matrix. If after we delete a row and a column of the same index, the nullity increases by one, we call that index a P-vertex of A.
Du Zhibin, da Fonseca Carlos M.
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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.
Rosario Fernandes, Henrique F da Cruz
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Linear Algebra and Its Applications, 2005 The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. Among all \(n\)-vertex trees, the star tree has greatest nullity (equal to \(n-2\)). In this paper it is shown that among all \(n\)-vertex trees whose vertex degrees do not exceed a fixed value \(D\), the greatest nullity is \(n- 2 \lceil (n-1)/D \rceil\).
Ivan Gutman, Irène Sciriha
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ZERO FORCING NUMBER AND MAXIMUM NULLITY OF GENERAL POWER GRAPHS [PDF]
Journal of Algebraic SystemsLet Γ = (V,E) be a simple and undirected graph. General power graph of Γ, shown by Pg(Γ), is a graph with the vertex set P(V (Γ))\ϕ. Also two distinct vertices of B and C are adjacent if and only if every b ∈ B is adjacent to every c ∈ C \{b} in Γ.
Fateme Kheiridosst, Ebrahim Vatandoost
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Compatible Forts and Maximum Nullity of a Graph
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 Fürst +2 more
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Maximum nullity and zero forcing number of graphs with rank at most 4
Cogent Mathematics & Statistics, 2018 Let G be a simple graph with n vertices. The rank of G is the number of non-zero eigenvalues of its adjacency matrix and denoted by rank(G).
Katayoun Nozari, H M Srivastava
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