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Mathematics, Applied
Fenglei Tian, Yiju Wang
Summary: This paper provides a full characterization of graphs with specific normalized Laplacian eigenvalues of multiplicity n - 3, resolving a previously unsolved problem and confirming that graphs with specific multiplicity can be determined by their normalized Laplacian spectra.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Computer Science, Information Systems
Milan Basic, Branko Arsic, Zoran Obradovic
Summary: This paper proposes a practical and computationally efficient method for estimating the Laplacian spectra of the Kronecker product of graphs, which extracts the estimates from the spectral properties of their factor graphs and exhibits better stability. Furthermore, novel theoretical results regarding the correlation coefficients of the estimated eigenvectors are presented.
INFORMATION SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Xingchao Zhu, Zhiyong Zhu
Summary: This paper studies the normalized Laplacian spectra and their applications of weighted level-4 Sierpinski graphs. By using the spectral decimation technique and theoretical matrix analysis, the relationship between the normalized Laplacian spectra for two successive generations is obtained. Closed-form expressions of Kemeny's constant and the number of spanning trees for the weighted level-4 Sierpinski graph are derived using the obtained recursive relation.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
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Mathematics, Applied
Serife Burcu Bozkurt Altindag, Igor Milovanovic, Emina Milovanovic, Marjan Matejic
Summary: This paper discusses the bounds of the sum of alpha-th powers of the normalized signless Laplacian eigenvalues of a connected graph. It also explores the results for special cases when alpha = 1/2 and alpha = -1.
Article
Mathematics
Sai-Nan Zheng, Xi Chen, Lily Li Liu, Yi Wang
Summary: We provide a characterization of eigenvalue inequalities between two Hermitian matrices using inertia indices, and apply it to classical eigenvalue inequalities for Hermitian matrices as well as a generalization for normalized Laplacian matrices of simple graphs.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics, Applied
Shaowei Sun, Kinkar Chandra Das
Summary: This paper investigates the multiplicity of normalized Laplacian eigenvalues in a simple graph G, and provides some necessary and sufficient conditions. It also discusses graphs with specific multiplicity values, and characterizes connected graphs with certain multiplicity values for sufficiently large n.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
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Physics, Multidisciplinary
Zunaira Kosar, Shahid Zaman, Wajid Ali, Asad Ullah
Summary: Spanning trees have diverse applications in computer science, graph theory, and network design, playing crucial roles in routing protocols, image processing, and wireless sensor networks.
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Mathematics
M. Rajesh Kannan, Shivaramakrishna Pragada
Summary: In this paper, the author introduces a method to construct cospectral bipartite graphs and extends it to generate larger classes of such graphs. Additionally, the author provides constructions of non-bipartite graphs that are cospectral for adjacency matrices but not necessarily for normalized Laplacian matrices.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics
Shaun Fallat, Seyed Ahmad Mojallal
Summary: By using the concepts of clique partitions and edge clique covers of graphs, this paper explores the corresponding incidence structures. The connection provides lower bounds on the negative eigenvalues and their multiplicities associated with the adjacency matrix, bounds on the incidence energy, and on the signless Laplacian energy for graphs. Furthermore, an extended version of an incidence matrix tied to an edge clique cover is applied to establish several classes of graphs that allow two distinct eigenvalues.
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Mathematics, Interdisciplinary Applications
Jia-Bao Liu, Jing Chen, Jing Zhao, Shaohui Wang
Summary: This paper studies the structure properties, eigenvalues, and the total number of spanning trees of the linear heptagonal networks H-n. By using the method of decompositions, the Laplacian spectrum of H-n is shown to be created by eigenvalues of matrices L-A and L-S of specific orders.
Article
Mathematics, Applied
S. B. Bozkurt Altindag, I. Z. Milovanovic, E. I. Milovanovic, M. M. Matejic
Summary: This paper investigates the Laplacian eigenvalues of a tree and defines the Wiener index and the modified hyper-Wiener index. The modified hyper-Wiener index is expressed in terms of the Wiener index and Laplacian eigenvalues, and some lower and upper bounds for the modified hyper-Wiener index are established.
DISCRETE APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Leyou Xu, Bo Zhou
Summary: This paper investigates the spectral properties of sum distance in strong digraphs, including the sum distance signless Laplacian matrix and the sum distance Laplacian matrix. For these matrices, the paper determines the digraphs that minimize and/or maximize eigenvalues in certain families of strong digraphs, with a particular focus on the second largest and/or smallest eigenvalues.
DISCRETE APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
M. Rajesh Kannan, Navish Kumar, Shivaramakrishna Pragada
Summary: This paper introduces the concept of complex unit gain graph and related theorems, analyzes the properties of balanced gain graphs, proposes the concepts of frustration number and frustration index, and gives bounds related to the smallest eigenvalue. It also provides multiple upper and lower bounds related to extremal eigenvalues of the graph parameters, and discusses signed graphs as special cases of T-gain graphs.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics
Fouzul Atik, M. Rajesh Kannan, Ravindra B. Bapat
Summary: The article discusses the relationship between weighted trees and distance matrices, including the connection between the rank of the weighted Laplacian matrix and trees, the necessary and sufficient conditions for the invertibility of the distance matrix with matrix weights, and some properties of the distance matrices of matrix weighted trees. Finally, it derives an interlacing inequality for the eigenvalues of distance and Laplacian matrices when using positive definite matrix weights.
LINEAR & MULTILINEAR ALGEBRA
(2021)
Article
Mathematics, Applied
Laura Abatangelo, Corentin Lena, Paolo Musolino
Summary: The paper provides a full series expansion of a generalization of the u-capacity related to the Dirichlet-Laplacian in dimension three and higher. The results extend the previous findings on the planar case and are applied to study the asymptotic behavior of perturbed eigenvalues when Dirichlet conditions are imposed on a small regular subset of the domain.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
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Computer Science, Hardware & Architecture
Yuan Lin, Zhongzhi Zhang
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Automation & Control Systems
Yi Qi, Zhongzhi Zhang, Yuhao Yi, Huan Li
IEEE TRANSACTIONS ON CYBERNETICS
(2019)
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Computer Science, Hardware & Architecture
Yi Qi, Yuhao Yi, Zhongzhi Zhang
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Computer Science, Theory & Methods
Yucheng Wang, Qi Bao, Zhongzhi Zhang
THEORETICAL COMPUTER SCIENCE
(2019)
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Computer Science, Information Systems
Yibin Sheng, Zhongzhi Zhang
IEEE TRANSACTIONS ON INFORMATION THEORY
(2019)
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Computer Science, Information Systems
Huan Li, Stacy Patterson, Yuhao Yi, Zhongzhi Zhang
IEEE TRANSACTIONS ON INFORMATION THEORY
(2020)
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Automation & Control Systems
Yuhao Yi, Zhongzhi Zhang, Stacy Patterson
IEEE TRANSACTIONS ON CYBERNETICS
(2020)
Proceedings Paper
Computer Science, Theory & Methods
Zuobai Zhang, Wanyue Xu, Zhongzhi Zhang
PROCEEDINGS OF THE 13TH INTERNATIONAL CONFERENCE ON WEB SEARCH AND DATA MINING (WSDM '20)
(2020)
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Computer Science, Hardware & Architecture
Yuan Lin, Zhongzhi Zhang
Proceedings Paper
Computer Science, Artificial Intelligence
Yujia Jin, Qi Bao, Zhongzhi Zhang
2019 19TH IEEE INTERNATIONAL CONFERENCE ON DATA MINING (ICDM 2019)
(2019)
Proceedings Paper
Computer Science, Theory & Methods
Huan Li, Richard Peng, Liren Shan, Yuhao Yi, Zhongzhi Zhang
WEB CONFERENCE 2019: PROCEEDINGS OF THE WORLD WIDE WEB CONFERENCE (WWW 2019)
(2019)
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Engineering, Multidisciplinary
Yi Qi, Zhongzhi Zhang
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2019)
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Automation & Control Systems
Stacy Patterson, Yuhao Yi, Zhongzhi Zhang
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS
(2019)
Proceedings Paper
Computer Science, Theory & Methods
Huan Li, Zhongzhi Zhang
SODA'18: PROCEEDINGS OF THE TWENTY-NINTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS
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Computer Science, Hardware & Architecture
Yi Qi, Huan Li, Zhongzhi Zhang