Results 11 to 20 of about 2,691 (126)
On real or integral skew Laplacian spectrum of digraphs
, 2020 For a simple connected graph G with n vertices and m edges, let −→ G be a digraph obtained by giving an arbitrary direction to the edges of G . In this paper, we consider the skew Laplacian matrix of a digraph −→ G and we obtain the skew Laplacian ...
S. Pirzada +2 more
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A trace bound for integer-diagonal positive semidefinite matrices
Special Matrices, 2020 We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.
Mitchell Lon
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Characteristic polynomials of some weighted graph bundles and its application to links
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 503-510, 1994., 1994 In this paper, we introduce weighted graph bundles and study their characteristic polynomial. In particular, we show that the characteristic polynomial of a weighted ‐bundles over a weighted graph G? can be expressed as a product of characteristic polynomials two weighted graphs whose underlying graphs are G As an application, we compute the signature ...
Moo Young Sohn, Jaeun Lee
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A note on distance spectral radius of trees
Special Matrices, 2017 The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. We determine the unique non-starlike non-caterpillar tree with maximal distance spectral radius.
Wang Yanna +3 more
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Small clique number graphs with three trivial critical ideals
Special Matrices, 2018 The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. Previously, they have been used in the understanding and characterizing of the graphs with critical group with few invariant factors ...
Alfaro Carlos A., Valencia Carlos E.
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On minimum algebraic connectivity of graphs whose complements are bicyclic
Open Mathematics, 2019 The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model ...
Liu Jia-Bao +3 more
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Graphs Whose Aα -Spectral Radius Does Not Exceed 2
Discussiones Mathematicae Graph Theory, 2020 Let A(G) and D(G) be the adjacency matrix and the degree matrix of a graph G, respectively. For any real α ∈ [0, 1], we consider Aα (G) = αD(G) + (1 − α)A(G) as a graph matrix, whose largest eigenvalue is called the Aα -spectral radius of G.
Wang Jian Feng +3 more
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On ordering of minimal energies in bicyclic signed graphs
Acta Universitatis Sapientiae: Informatica, 2021 Let S = (G, σ) be a signed graph of order n and size m and let x1, x2, ..., xn be the eigenvalues of S. The energy of S is defined as ɛ(S)=∑j=1n|xj|\varepsilon \left( S \right) = \sum\limits_{j = 1}^n {\left| {{x_j}} \right|}. A connected signed graph is
Pirzada S. +2 more
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Rank relations between a {0, 1}-matrix and its complement
Open Mathematics, 2018 Let A be a {0, 1}-matrix and r(A) denotes its rank. The complement matrix of A is defined and denoted by Ac = J − A, where J is the matrix with each entry being 1.
Ma Chao, Zhong Jin
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Spectral Conditions for Graphs to be k-Hamiltonian or k-Path-Coverable
Discussiones Mathematicae Graph Theory, 2020 A graph G is k-Hamiltonian if for all X ⊂ V (G) with |X| ≤ k, the subgraph induced by V (G) \ X is Hamiltonian. A graph G is k-path-coverable if V (G) can be covered by k or fewer vertex disjoint paths.
Liu Weijun +3 more
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