منابع مشابه
Median eigenvalues of bipartite graphs
For a graph G of order n and with eigenvalues λ1 > · · · > λn, the HL-index R(G) is defined as R(G) = max { |λb(n+1)/2c|, |λd(n+1)/2e| } . We show that for every connected bipartite graph G with maximum degree ∆ > 3, R(G) 6 √ ∆− 2 unless G is the the incidence graph of a projective plane of order ∆− 1. We also present an approach through graph covering to construct infinite families of bipartit...
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For a commutative semigroup S with 0, the zero-divisor graph of S denoted by &Gamma(S) is the graph whose vertices are nonzero zero-divisor of S, and two vertices x, y are adjacent in case xy = 0 in S. In this paper we study median and center of this graph. Also we show that if Ass(S) has more than two elements, then the girth of &Gamma(S) is three.
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Graph embeddings are useful in bounding the smallest nontrivial eigenvalues of Laplacian matrices from below. For an n×n Laplacian, these embedding methods can be characterized as follows: The lower bound is based on a clique embedding into the underlying graph of the Laplacian. An embedding can be represented by a matrix Γ; the best possible bound based on this embedding is n/λmax(Γ Γ). Howeve...
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In 1993 Hong asked what are the best bounds on the k’th largest eigenvalue λk(G) of a graph G of order n. This challenging question has never been tackled for any 2 < k < n. In the present paper tight bounds are obtained for all k > 2, and even tighter bounds are obtained for the k’th largest singular value λk(G). Some of these bounds are based on Taylor’s strongly regular graphs, and other on ...
متن کاملInvertibility of graph translation and support of Laplacian Fiedler vectors
The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian eigenvalues and eigenvectors. We extend these results and prove that the translation operator to the i’th node is invertible if and only if all eigenvectors ar...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2017
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.10.020