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Graphs with three distinct distance eigenvalues
Applied Mathematics and Computation, 2023 In this paper, some special distance spectral properties of graphs are considered. Concretely, we recursively construct an infinite family of trees with distance eigenvalue $-1$, and determine all $\{C_3,C_4\}$-free connected graphs with three distinct distance eigenvalues of which the smallest one is equal to $-3$, which partially answers a problem ...
Zhang, Yuke, Lin, Huiqiu
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Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph [PDF]
Journal of Inequalities and Applications, 2018 Let G be a connected graph of order n. The remoteness of G, denoted by ρ, is the maximum average distance from a vertex to all other vertices. Let [Formula: see text], [Formula: see text] and [Formula: see text] be the distance, distance Laplacian and distance signless Laplacian eigenvalues of G, respectively.
Huicai Jia, Hongye Song
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On the second largest distance eigenvalue [PDF]
Linear and Multilinear Algebra, 2016 We characterize all connected graphs whose second largest distance eigenvalues belong to , as well as all trees whose second distance eigenvalues belong to . We also consider unicyclic graphs whose second distance eigenvalues belong to .
Rundan Xing, Bo Zhou
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Distance Signless Laplacian Eigenvalues, Diameter, and Clique Number
Discrete Mathematics Letters, 2022 Summary: Let \(G\) be a connected graph of ordern. Let \(\operatorname{Diag}(\mathrm{Tr})\) be the diagonal matrix of vertex transmissions and let \(\mathcal{D}(G)\) be the distance matrix of \(G\). The distance signless Laplacian matrix of \(G\) is defined as \(\mathcal{D}^{\mathcal{Q}}(G) =\operatorname{Diag}(\mathrm{Tr}) + \mathcal{D}(G)\) and the ...
Saleem Khan, Shariefuddin Pirzada
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Distance (Signless) Laplacian Eigenvalues of $k$-uniform Hypergraphs
Taiwanese Journal of Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xiangxiang, Wang, Ligong
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Bounds on distances between eigenvalues
Linear Algebra and its Applications, 1984 This paper presents bounds for the distances between a given real eigenvalue \(\lambda\) of a real square matrix A and its remaining eigenvalues. In the main result these bounds are given in terms of a norm of the matrix A-\(\lambda\) I and its Drazin inverse, respectively, on the subspace orthogonal to an eigenvector corresponding to \(\lambda\). Some
Haviv, Moshe, Rothblum, Uriel G.
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Distance Eigenvalues and Forwarding Indices of Circulants
Taiwanese Journal of Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Shuting, Lin, Huiqiu, Shu, Jinlong
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On Least Distance Eigenvalue of Uniform Hypergraphs
Taiwanese Journal of Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Hongying, Zhou, Bo
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Distance-regular Cayley graphs with least eigenvalue $-2$
Designs Codes and Cryptography, 2015 13 pages, On line paper as open access to publish in Des.
van Dam, Edwin R. +2 more
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On the distance and distance Laplacian eigenvalues of graphs
Linear Algebra and its Applications, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Huiqiu +3 more
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