Results 201 to 210 of about 2,177,028 (229)
Are We Chasing a Wild Goose? Rethinking Breeding Targets for Salinity Stress Tolerance in Rice. [PDF]
Plants (Basel)Xu Q +8 more
europepmc +1 more source
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 ...
John Hutchens +2 more
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Techniques for Determining Equality of the Maximum Nullity and the Zero Forcing Number of a Graph [PDF]
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.
Derek Young
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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, Irene Sciriha
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On the Maximum Positive Semi-Definite Nullity and the Cycle Matroid of Graphs [PDF]
Electronic Journal of Linear Algebra, 2009 Let G = (V,E) be a graph with V = {1, 2, ¿ ,n}, in which we allow parallel edges but no loops, and let S+(G) be the set of all positive semi-definite n × n matrices A = [ai,j] with ai,j = 0 if i ¿ j and i and j are non-adjacent, ai,j ¿ 0 if i ¿ j and i and j are connected by exactly one edge, and ai,j e if i = j or i and j are connected by parallel ...
Heindricus van der Holst
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Tree Cover Number and Maximum Semidefinite Nullity of Some Graph Classes [PDF]
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 $G$.
Sivaram Narayan, Rachel Domagalski
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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 and Zero Forcing Number on Graphs With Maximum Degree at Most Three
Discrete Applied Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Meysam Alishahi
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Line Graphs: Their Maximum Nullities and Zero Forcing Numbers [PDF]
Czechoslovak Mathematical Journal, 2016 The main aim of this paper is to analyze the maximum nullity and zero forcing number, and their positive counterparts, for general families of line graphs associated with graphs possessing some specific properties. In [\textit{F. Barioli} et al., Linear Algebra Appl. 428, No.
Shaun Michael Fallat
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