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Journal articles on the topic 'Connectivity eigenvalue'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Abiad, Aida, Boris Brimkov, Xavier Martinez-Rivera, Suil O, and Jingmei Zhang. "Spectral Bounds for the Connectivity of Regular Graphs with Given Order." Electronic Journal of Linear Algebra 34 (February 21, 2018): 428–43. http://dx.doi.org/10.13001/1081-3810.3675.

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The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, two upper bounds are presented for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degre

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2

Manickam, Machasri, and Kalyani Desikan. "Relationship Between the Second Largest Adjacency and Signless Laplacian Eigenvalues of Graphs and Properties of Planar Graphs." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 3004–21. https://doi.org/10.29020/nybg.ejpam.v17i4.5364.

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A graph’s second largest eigenvalue is a significant algebraic characteristic that provides details on the graph’s expansion, connectivity, and randomness. Bounds for the second largest eigenvalue of a graph, denoted as λ2 were previously established in the literature in relation to graph parameters like edge connectivity and vertex connectivity, matching number, independencenumber, and edge expansion constant, among others. A graph is planar if it can be drawn in a plane without graph edges crossing. Determining the planarity of a graph helps in optimizing, simplifying, and understanding comp

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3

Rangasamy, Buvaneswari, Senbaga Priya Karuppusamy, and Farshid Mofidnakhaei. "Novel Spectral Conditions for Diagonalizability and Connectivity in Spectral Fuzzy Graph Theory." Journal of Physical Sciences 29, no. 00 (2024): 47–59. https://doi.org/10.62424/jps.2024.29.00.06.

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This paper explores the properties of fuzzy matrices in fuzzy graphs and the conditions for the diagonalizability of fuzzy matrices. Necessary and sufficient conditions for fuzzy graphs to have non-negative and distinct eigenvalues are provided, and the existence of orthogonal eigenvectors corresponding to distinct eigenvalues in fuzzy matrices are discussed. Also, conditions for the second smallest eigenvalue of the Laplacian matrix are established to ensure connectivity in fuzzy graphs.

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Qu, Jijun, Zhijian Ji, Chong Lin, and Haisheng Yu. "Fast Consensus Seeking on Networks with Antagonistic Interactions." Complexity 2018 (December 16, 2018): 1–15. http://dx.doi.org/10.1155/2018/7831317.

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It is well known that all agents in a multiagent system can asymptotically converge to a common value based on consensus protocols. Besides, the associated convergence rate depends on the magnitude of the smallest nonzero eigenvalue of Laplacian matrix L. In this paper, we introduce a superposition system to superpose to the original system and study how to change the convergence rate without destroying the connectivity of undirected communication graphs. And we find the result if the eigenvector x of eigenvalue λ has two identical entries xi=xj, then the weight and existence of the edge eij d

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Alshamary, Bader, Milica Anđelić, Edin Dolićanin, and Zoran Stanić. "Controllable multi-agent systems modeled by graphs with exactly one repeated degree." AIMS Mathematics 9, no. 9 (2024): 25689–704. http://dx.doi.org/10.3934/math.20241255.

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<p>We consider the controllability of multi-agent dynamical systems modeled by a particular class of bipartite graphs, called chain graphs. Our main focus is related to chain graphs with exactly one repeated degree. We determine all chain graphs with this structural property and derive some properties of their Laplacian eigenvalues and associated eigenvectors. On the basis of the obtained theoretical results, we compute the minimum number of leading agents that make the system in question controllable and locate the leaders in the corresponding graph. Additionaly, we prove that a chain g

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6

Sun, Yan, and Faxu Li. "Algebraic Connectivity and Disjoint Vertex Subsets of Graphs." Mathematical Problems in Engineering 2020 (July 31, 2020): 1–6. http://dx.doi.org/10.1155/2020/5763218.

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It is well known that the algebraic connectivity of a graph is the second small eigenvalue of its Laplacian matrix. In this paper, we mainly research the relationships between the algebraic connectivity and the disjoint vertex subsets of graphs, which are presented through some upper bounds on algebraic connectivity.

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Manickam, Machasri, and Kalyani Desikan. "Eigenvalue Interlacing of Bipartite Graphs and Construction of Expander Code using Vertex-split of a Bipartite Graph." European Journal of Pure and Applied Mathematics 17, no. 2 (2024): 772–89. http://dx.doi.org/10.29020/nybg.ejpam.v17i2.5057.

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The second largest eigenvalue of a graph is an important algebraic parameter which is related with the expansion, connectivity and randomness properties of a graph. Expanders are highly connected sparse graphs. In coding theory, Expander codes are Error Correcting codes made up of bipartite expander graphs. In this paper, first we prove the interlacing of the eigenvalues of the adjacency matrix of the bipartite graph with the eigenvalues of the bipartite quotient matrices of the corresponding graph matrices. Then we obtain bounds for the second largest and second smallest eigenvalues. Since th

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8

Wen, Zhiyong, Xiaoxiong Weng, and Pengfei Zhang. "Evaluating the Connectivity and Imbalance Contribution of New Sections towards Highway Network: A Complex Network Perspective." Journal of Advanced Transportation 2023 (November 1, 2023): 1–13. http://dx.doi.org/10.1155/2023/6616512.

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The evaluation of the impacts of new sections on the highway network is an essential aspect of the feasibility study. Existing studies predominantly concentrated on engineering-oriented feasibility assessments, often overlooking their potential effects on parallel sections and the overall network. In this research, we present an evaluation model for new sections based on complex networks, focusing on the connectivity and imbalance of transportation networks. This model serves as a supplementary approach for enhancing the feasibility analysis of new highway projects. The model comprises three d

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9

Liu, Huiqing, Mei Lu, and Feng Tian. "Edge-connectivity and (signless) Laplacian eigenvalue of graphs." Linear Algebra and its Applications 439, no. 12 (2013): 3777–84. http://dx.doi.org/10.1016/j.laa.2013.10.017.

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10

Ye, Miao-Lin, Yi-Zheng Fan, and Dong Liang. "The least eigenvalue of graphs with given connectivity." Linear Algebra and its Applications 430, no. 4 (2009): 1375–79. http://dx.doi.org/10.1016/j.laa.2008.10.031.

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11

Kuruzov, I. A., A. V. Rogozin, S. A. Chezhegov, and A. B. Kupavskii. "ROBUST ALGEBRAIC CONNECTIVITY." Программирование, no. 6 (November 1, 2023): 49–59. http://dx.doi.org/10.31857/s0132347423060067.

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The second smallest eigenvalue of a graph Laplacian is known as algebraic connectivity of the graph. This value shows how much this graph is connected. But this metric does not take into attention possible changes in graph. Note, that deletion of even one node or edge can lead the graph to be disconnected. This work is devoted to development of a metric that should describe robustness of the graph to such changes. All proposed metrics are based on algebraic connectivity. Besides, we provide generalization of some famous optimization methods for our robust modifications of algebraic connectivit

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12

Yu, Guihai, and Xinzhuang Chen. "Network Similarity Measure and Ediz Eccentric Connectivity Index." Complexity 2020 (December 3, 2020): 1–9. http://dx.doi.org/10.1155/2020/2567570.

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Network similarity measures have proven essential in the field of network analysis. Also, topological indices have been used to quantify the topology of networks and have been well studied. In this paper, we employ a new topological index which we call the Ediz eccentric connectivity index. We use this quantity to define network similarity measures as well. First, we determine the extremal value of the Ediz eccentric connectivity index on some network classes. Second, we compare the network similarity measure based on the Ediz eccentric connectivity index with other well-known topological indi

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13

Liu, Hongjuan, and Honghai Li. "Normalized algebraic connectivity of graphs." Discrete Mathematics, Algorithms and Applications 11, no. 03 (2019): 1950031. http://dx.doi.org/10.1142/s1793830919500319.

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Let [Formula: see text] be the second smallest normalized Laplacian eigenvalue of a graph [Formula: see text], called the normalized algebraic connectivity of [Formula: see text]. In this paper, we study the relation between the normalized algebraic connectivity of the coalescence of two graphs and that of these two graphs. Furthermore, we investigate how the normalized algebraic connectivity behaves when the graph is perturbed by relocating pendent edges.

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14

SHANG, YILUN. "The natural connectivity of colored random graphs." Creative Mathematics and Informatics 20, no. 2 (2011): 197–202. http://dx.doi.org/10.37193/cmi.2011.02.11.

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The natural connectivity as a robustness measure of complex network has been proposed recently. It can be regarded as the average eigenvalue obtained from the graph spectrum. In this paper, we introduce an inhomogeneous random graph model, G(n, {ci}, {pi}), and investigate its natural connectivity. Binomial random graph ... . Simulations are performed to validate our theoretical results.

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15

Jiang, Guisheng, Guidong Yu, and Jinde Cao. "The Least Algebraic Connectivity of Graphs." Discrete Dynamics in Nature and Society 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/756960.

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The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose complements are trees, but not stars, and among all graphs whose complements are unicyclic graphs, but not stars adding one edge, respectively.

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16

Hu, Yu, and Haim Sompolinsky. "The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics." PLOS Computational Biology 18, no. 7 (2022): e1010327. http://dx.doi.org/10.1371/journal.pcbi.1010327.

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A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the network dynamics’ Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in a randomly connected recurrent network of stochastic neurons. An exact analytic

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17

Pan, Jing-Jing, Michael G. H. Bell, Kam-Fung Cheung, Supun Perera, and Hang Yu. "Connectivity analysis of the global shipping network by eigenvalue decomposition." Maritime Policy & Management 46, no. 8 (2019): 957–66. http://dx.doi.org/10.1080/03088839.2019.1647587.

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18

O, Suil. "The second largest eigenvalue and vertex-connectivity of regular multigraphs." Discrete Applied Mathematics 279 (May 2020): 118–24. http://dx.doi.org/10.1016/j.dam.2019.10.010.

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19

Bonaccorsi, Giacomo, Matteo Pozzi, Jaeyub Hyun, Hyunsun Alicia Kim, and Francesco Braghin. "Connectivity constraints for eigenvalue reduction in level-set topology optimization." Computers & Structures 316 (September 2025): 107865. https://doi.org/10.1016/j.compstruc.2025.107865.

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20

Li, Gang, Yonghua Jiang, Weidong Jiao, et al. "The Maximum Eigenvalue of the Brain Functional Network Adjacency Matrix: Meaning and Application in Mental Fatigue Evaluation." Brain Sciences 10, no. 2 (2020): 92. http://dx.doi.org/10.3390/brainsci10020092.

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The maximum eigenvalue of the adjacency matrix (AM) has been supposed to contain rich information about the corresponding network. An experimental study focused on revealing the meaning and application of the maximum eigenvalue is missing. To this end, AM was constructed using mutual information (MI) to determine the functional connectivity with electroencephalogram (EEG) data recorded with a mental fatigue model, and then was converted into both binary and weighted brain functional network (BFN) and corresponding random networks (RNs). Both maximum eigenvalue and corresponding network charact

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21

Arsic, Branko, Dragos Cvetkovic, Slobodan Simic, and Milan Skaric. "Graph spectral techniques in computer sciences." Applicable Analysis and Discrete Mathematics 6, no. 1 (2012): 1–30. http://dx.doi.org/10.2298/aadm111223025a.

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We give a survey of graph spectral techniques used in computer sciences. The survey consists of a description of particular topics from the theory of graph spectra independently of the areas of Computer science in which they are used. We have described the applications of some important graph eigenvalues (spectral radius, algebraic connectivity, the least eigenvalue etc.), eigenvectors (principal eigenvector, Fiedler eigenvector and other), spectral reconstruction problems, spectra of random graphs, Hoffman polynomial, integral graphs etc. However, for each described spectral technique we indi

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22

Tan, S. Y., J. Wu, M. J. Li, and X. Lu. "Approximating natural connectivity of scale-free networks based on largest eigenvalue." EPL (Europhysics Letters) 114, no. 5 (2016): 58002. http://dx.doi.org/10.1209/0295-5075/114/58002.

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23

Ma, Tingyan, Ligong Wang, and Yang Hu. "The vertex connectivity and the third largest eigenvalue in regular (multi-)graphs." Electronic Journal of Linear Algebra 40 (March 8, 2024): 322–32. http://dx.doi.org/10.13001/ela.2024.7977.

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Let $G$ be a simple graph or a multigraph. The vertex connectivity $\kappa(G)$ of $G$ is the minimum size of a vertex set $S$ such that $G-S$ is disconnected or has only one vertex. We denote by $\lambda_{3}(G)$ the third largest eigenvalue of the adjacency matrix of $G$. In this paper, we present an upper bound for $\lambda_{3}(G)$ in a $d$-regular (multi-)graph $G$ which guarantees that $\kappa(G)\geq t+1$, which is based on the result of Abiad et al. [Spectral bounds for the connectivity of regular graphs with given order. Electron. J. Linear Algebra 34:428-443, 2018]. Furthermore, we impro

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24

ZHAO, FUQIANG, LICHAO ZHANG, GUIJUN YANG, LI HE, and FENGYU YAN. "APPLICATION OF CUT ALGORITHM BASED ON ALGEBRAIC CONNECTIVITY TO COMMUNITY DETECTION." Advances in Complex Systems 20, no. 01 (2017): 1750002. http://dx.doi.org/10.1142/s0219525917500023.

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In the graph of a complex network, the algebraic connectivity is the second smallest eigenvalue of a Laplacian matrix. In this paper, we present a cut algorithm based on edge centrality by minimizing the algebraic connectivity of graph. The edge centrality cut algorithm (ECCA) cuts [Formula: see text] edges at a time in order to reduce temporal complexity, the algebraic connectivity of which experiences the fastest decline. To prevent nodes from overcutting, each edge sets the weight. We use the advanced ECCA (AECCA) to detect overlapping communities by calculating the correlation coefficients

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25

Xing, En Jun, Fu Qiang Zhao, Shuo Zhang, and Xin Yu Ge. "Research of Edge Centrality Based on the Algebraic Connectivity." Applied Mechanics and Materials 543-547 (March 2014): 3636–40. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.3636.

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In connected graph, edge centrality represents the importance of edge and loading degree in the process of information transmission. The second eigenvalue of Laplacian matrix decides connectivity of complex networks. We propose edge centrality model and cut model based on minimization model of the algebraic connectivity. Edge centrality function is derived in order to calculate edge centrality. Cut model deletes k edges at an iteration whose algebraic connectivity of complex networks decreased fastest. Choice of k is based on edge sparse degree of complex networks. By empirical analysis of rea

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26

Akhter, Sadia, Mattia Frasca, and Ernesto Estrada. "Golden Laplacian Graphs." Mathematics 12, no. 4 (2024): 613. http://dx.doi.org/10.3390/math12040613.

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Many properties of the structure and dynamics of complex networks derive from the characteristics of the spectrum of the associated Laplacian matrix, specifically from the set of its eigenvalues. In this paper, we show that there exist graphs for which the ratio between the length of the spectrum (that is, the difference between the largest and smallest eigenvalues of the Laplacian matrix) and its spread (the difference between the second smallest eigenvalue and the smallest one) is equal to the golden ratio. We call such graphs Golden Laplacian Graphs (GLG). In this paper, we first find all s

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27

Wang, Chunxiang, та Shaohui Wang. "The Aα-Spectral Radii of Graphs with Given Connectivity". Mathematics 7, № 1 (2019): 44. http://dx.doi.org/10.3390/math7010044.

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The A α -matrix is A α ( G ) = α D ( G ) + ( 1 − α ) A ( G ) with α ∈ [ 0 , 1 ] , given by Nikiforov in 2017, where A ( G ) is adjacent matrix, and D ( G ) is its diagonal matrix of the degrees of a graph G. The maximal eigenvalue of A α ( G ) is said to be the A α -spectral radius of G. In this work, we determine the graphs with largest A α ( G ) -spectral radius with fixed vertex or edge connectivity. In addition, related extremal graphs are characterized and equations satisfying A α ( G ) -spectral radius are proposed.

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28

LIU, G. R., X. L. CHEN, and J. N. REDDY. "BUCKLING OF SYMMETRICALLY LAMINATED COMPOSITE PLATES USING THE ELEMENT-FREE GALERKIN METHOD." International Journal of Structural Stability and Dynamics 02, no. 03 (2002): 281–94. http://dx.doi.org/10.1142/s0219455402000634.

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An element free Galerkin (EFG) method is presented for buckling analyses of isotropic and symmetrically laminated composite plates using the classical plate theory. The shape functions are constructed using the moving least squares (MLS) approximation, and no element connectivity among nodes is required. The deflection can be easily approximated with higher-order polynomials as desired. The discrete eigenvalue problem is derived using the principle of minimum total potential energy of the system. The essential boundary conditions are introduced into the formulation through the use of the Lagra

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29

Wang, Long, Chunyu Yan, Xianwen Fang, Xianya Geng, and Fenglei Tian. "Vertex-connectivity, chromatic number, domination number, maximum degree and Laplacian eigenvalue distribution." Linear Algebra and its Applications 607 (December 2020): 307–18. http://dx.doi.org/10.1016/j.laa.2020.08.011.

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30

Križmančić, Marko, and Stjepan Bogdan. "Adaptive connectivity control in networked multi-agent systems: A distributed approach." PLOS ONE 19, no. 12 (2024): e0314642. https://doi.org/10.1371/journal.pone.0314642.

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Effective communication is crucial for the performance and collaboration within cooperative networked multi-agent systems. However, existing literature lacks comprehensive solutions for dynamically monitoring and adjusting communication topologies to balance connectivity and energy efficiency. This study addresses this gap by proposing a distributed approach for estimating and controlling system connectivity over time. We introduce a modified consensus protocol where agents exchange local assessments of communication link quality, enabling the estimation of a global weighted adjacency matrix w

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31

XING Zihan, LIU Siyu, LIU Hui, and CHEN Lingxiao. "An Algorithm for Mining Key Node Groups in Large-Scale Complex Networks Based on Spectral Graph Theory." Acta Physica Sinica 74, no. 16 (2025): 0. https://doi.org/10.7498/aps.74.20250416.

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In this paper, we investigate node group significance identification in undirected complex networks by utilizing spectral graph theory of pinning control. Building upon the node significance criterion in network pinning control theory-where important controlled nodes are those maximizing the minimum eigenvalue of the grounded Laplacian matrix after their removal. We propose MFG (Multi-metric Fusion and enhanced Greedy search), a novel key node group identification framework that integrates multi-metric linear fusion and an enhanced greedy search strategy. The methodology initiates by construct

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32

Alwafi, Fatma A. S., Xu Xu, Reza Saatchi, and Lyuba Alboul. "Development and Evaluation of a Multi-Robot Path Planning Graph Algorithm." Information 16, no. 6 (2025): 431. https://doi.org/10.3390/info16060431.

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A new multi-robot path planning (MRPP) algorithm for 2D static environments was developed and evaluated. It combines a roadmap method, utilising the visibility graph (VG), with the algebraic connectivity (second smallest eigenvalue (λ2)) of the graph’s Laplacian and Dijkstra’s algorithm. The paths depend on the planning order, i.e., they are in sequence path-by-path, based on the measured values of algebraic connectivity of the graph’s Laplacian and the determined weight functions. Algebraic connectivity maintains robust communication between the robots during their navigation while avoiding c

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33

HENKEL, MALTE, and VLADIMIR PRIVMAN. "LONGITUDINAL CORRELATION LENGTH IN DIRECTED PERCOLATION AND RELATED MODELS: A POSSIBLE NEW SCALING MECHANISM." Modern Physics Letters B 05, no. 08 (1991): 555–59. http://dx.doi.org/10.1142/s0217984991000666.

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The finite-size scaling of the correlation length for directed and undirected systems is reviewed with emphasis on the asymptotic eigenvalue degeneracy associated with long-range order or long-range connectivity. The standard scaling mechanism for matching asymptotic behaviors on approach to criticality applies for Ising and other models. However, numerical evidence suggests that for directed percolation in 2D a modified formulation is appropriate, incorporating irrelevant-variable corrections in a new pattern of asymptotic scaling.

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34

Das, Kinkar, and Muhuo Liu. "Minimal extremal graphs for addition of algebraic connectivity and independence number of connected graphs." Filomat 31, no. 18 (2017): 5545–51. http://dx.doi.org/10.2298/fil1718545c.

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Let G = (V,E) be a simple connected graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the Laplacian matrix of graph G is L(G) = D(G)-A(G). Let a(G) and ?(G), respectively, be the second smallest Laplacian eigenvalue and the independence number of graph G. In this paper, we characterize the extremal graph with second minimum value for addition of algebraic connectivity and independence number among all connected graphs with n ? 6 vertices (Actually, we can determine the p-th minimum value of a(G)+ ?(G) under certain condition when p is small)

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35

V, Dhananjayamurthy B., Murthy K. B, Komala C. S, Nagarathnamma K. G, and Amruthalakshmi M. R. "Quantitative Structure Property Relationship Modeling Of Certain Novel Anticancer Drugs Using Molecular Descriptors." International Journal of Environmental Sciences 11, no. 7s (2025): 1023–35. https://doi.org/10.64252/w9d56g51.

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A topological index is a numerical value linked to molecular graphs, capable of predicting the physicochemical and biological properties of various anticancer medications, such as those used for treating blood, breast, and skin cancers. In this paper, intercorrelation between the Balban index B(G), connective eccentric index (CEI), eccentricity connectivity index (ECI), harmonic index (H(G)), hyper Zagreb index , first path Zagreb index ( ), second path Zagreb index ( ), Randic index ( ), sum connectivity index (SCI(G)), graph energy (E(G)) and Laplacian energy (LE(G)) is studied on the set of

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36

Herbert, Elizabeth, and Srdjan Ostojic. "The impact of sparsity in low-rank recurrent neural networks." PLOS Computational Biology 18, no. 8 (2022): e1010426. http://dx.doi.org/10.1371/journal.pcbi.1010426.

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Neural population dynamics are often highly coordinated, allowing task-related computations to be understood as neural trajectories through low-dimensional subspaces. How the network connectivity and input structure give rise to such activity can be investigated with the aid of low-rank recurrent neural networks, a recently-developed class of computational models which offer a rich theoretical framework linking the underlying connectivity structure to emergent low-dimensional dynamics. This framework has so far relied on the assumption of all-to-all connectivity, yet cortical networks are know

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Liu, Jia-Bao, Muhammad Javaid, Mohsin Raza, and Naeem Saleem. "On minimum algebraic connectivity of graphs whose complements are bicyclic." Open Mathematics 17, no. 1 (2019): 1490–502. http://dx.doi.org/10.1515/math-2019-0119.

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Abstract 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, synchronize the stability, analyze the diffusion processes and find the connectivity of the graphs (networks). A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, firstly the unique graph with a minimum algebraic connectivity is character

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38

Levin, R. I., T. P. Waters, and N. A. J. Lieven. "Required Precision and Valid Methodologies for Dynamic Finite Element Model Updating." Journal of Vibration and Acoustics 120, no. 3 (1998): 733–41. http://dx.doi.org/10.1115/1.2893891.

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This paper investigates the effects of adjusting the system matrices of a Finite Element (FE) model on the eigen-properties of the model for the purposes of dynamic model updating. It is shown that minor modifications to the connectivity of the model can cause unexpectedly significant eigenvalue perturbations of the lower modes, especially if the physical location of the modification is near an antinode of vibration of a lower mode. These modifications can be introduced either by non-parametric updating techniques or unwittingly by truncation of the FE structural matrices. It is proposed that

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39

M C, Jayaprakash, Dhananjayamurthy B V, Nagarathnamma K G, Mohammad Fareeduddin, and Amruthalakshmi M R. "QUANTITATIVE STRUCTURE PROPERTY RELATIONSHIP MODELING OF CERTAIN NOVEL ANTICANCER DRUGS USING MOLECULAR DESCRIPTORS." Journal of Dynamics and Control 9, no. 5 (2025): 92–106. https://doi.org/10.71058/jodac.v9i5009.

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A topological index is a numerical value linked to molecular graphs, capable of predicting the physicochemical and biological properties of various anticancer medications, such as those used for treating blood, breast, and skin cancers. In this paper, intercorrelation between the Balban index B(G), connective eccentric index (CEI), eccentricity connectivity index (ECI), harmonic index (H(G)), hyper Zagreb index HZ(G), first path Zagreb index (FP_1), second path Zagreb index (FP_2), Randic index (R(G)), sum connectivity index (SCI(G)), graph energy (E(G)) and Laplacian energy (LE(G)) is studied

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40

Banerjee, Subarsha. "Laplacian spectrum of comaximal graph of the ring ℤ_n". Special Matrices 10, № 1 (2022): 285–98. http://dx.doi.org/10.1515/spma-2022-0163.

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Abstract In this paper, we study the interplay between the structural and spectral properties of the comaximal graph Γ ( Z n ) \Gamma \left({{\mathbb{Z}}}_{n}) of the ring Z n {{\mathbb{Z}}}_{n} for n > 2 n\gt 2 . We first determine the structure of Γ ( Z n ) \Gamma \left({{\mathbb{Z}}}_{n}) and deduce some of its properties. We then use the structure of Γ ( Z n ) \Gamma \left({{\mathbb{Z}}}_{n}) to deduce the Laplacian eigenvalues of Γ ( Z n ) \Gamma \left({{\mathbb{Z}}}_{n}) for various n n . We show that Γ ( Z n ) \Gamma \left({{\mathbb{Z}}}_{n}) is Laplacian integral for n = p α q β n={

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Maliassov, Serguei Yu, and Yuri V. Vassilevski. "Extracting connectivity paths in digital core images using solution of partial minimum eigenvalue problem." Russian Journal of Numerical Analysis and Mathematical Modelling 38, no. 6 (2023): 373–80. http://dx.doi.org/10.1515/rnam-2023-0028.

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Abstract We show theoretically and numerically that the lowest non-trivial eigenvector function for a specific eigenproblem has almost constant values in high conductivity channels, which are different in separate channels. Therefore, based on these distinct values, all separate connected clusters of open pores can be identified in digital cores.

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Qian, Wei, and Lei Wang. "Eigenvalue Based Approach for Global Consensus in Multiagent Systems with Nonlinear Dynamics." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/407269.

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This paper addresses the global consensus of nonlinear multiagent systems with asymmetrically coupled identical agents. By employing a Lyapunov function and graph theory, a sufficient condition is presented for the global exponential consensus of the multiagent system. The analytical result shows that, for a weakly connected communication graph, the algebraic connectivity of a redefined symmetric matrix associated with the directed graph is used to evaluate the global consensus of the multiagent system with nonlinear dynamics under the common linear consensus protocol. The presented condition

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R. Stella Maragatham. "Analysis of Graph Inverses and Algebraic Connectivity in a Systematic Way." Communications on Applied Nonlinear Analysis 32, no. 3 (2024): 525–38. http://dx.doi.org/10.52783/cana.v32.2013.

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an exhaustive and methodical study of algebraic connectedness and graph inverses. In many contexts, graph theory plays a crucial role, particularly when understanding intricate systems. This paper delves into the fundamental concepts of graph inverses and explains their significance for network analysis and connectivity evaluation. The Laplacian lattice's second-smallest eigenvalue, or algebraic connectivity µN−1, plays a crucial role in some features like network heartiness, synchronisation security, and diffusion processes. In this study, we focus on the algebraic connectedness in the networ

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Ren, Jingyao, Eric Ewing, T. K. Satish Kumar, Sven Koenig, and Nora Ayanian. "Map Connectivity and Empirical Hardness of Grid-based Multi-Agent Pathfinding Problem." Proceedings of the International Conference on Automated Planning and Scheduling 34 (May 30, 2024): 484–88. http://dx.doi.org/10.1609/icaps.v34i1.31508.

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We present an empirical study of the relationship between map connectivity and the empirical hardness of the multi-agent pathfinding (MAPF) problem. By analyzing the second smallest eigenvalue (commonly known as lambda2) of the normalized Laplacian matrix of different maps, our initial study indicates that maps with smaller lambda2 tend to create more challenging instances when agents are generated uniformly randomly. Additionally, we introduce a map generator based on Quality Diversity (QD) that is capable of producing maps with specified lambda2 ranges, offering a possible way for generating

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MORA, JUAN CARLOS SECK TUOH, SERGIO V. CHAPA VERGARA, GENARO JUÁREZ MARTÍNEZ, and HAROLD V. McINTOSH. "SPECTRAL PROPERTIES OF REVERSIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA." International Journal of Modern Physics C 14, no. 03 (2003): 379–95. http://dx.doi.org/10.1142/s0129183103004541.

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Reversible cellular automata are invertible dynamical systems characterized by discreteness, determinism and local interaction. This article studies the local behavior of reversible one-dimensional cellular automata by means of the spectral properties of their connectivity matrices. We use the transformation of every one-dimensional cellular automaton to another of neighborhood size 2 to generalize the results exposed in this paper. In particular we prove that the connectivity matrices have a single positive eigenvalue equal to 1; based on this result we also prove the idempotent behavior of t

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Wu, Zhihong, Erhan Hai, Zhengyang Di, et al. "Using WGCNA (weighted gene co-expression network analysis) to identify the hub genes of skin hair follicle development in fetus stage of Inner Mongolia cashmere goat." PLOS ONE 15, no. 12 (2020): e0243507. http://dx.doi.org/10.1371/journal.pone.0243507.

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Objective Mature hair follicles represent an important stage of hair follicle development, which determines the stability of hair follicle structure and its ability to enter the hair cycle. Here, we used weighted gene co-expression network analysis (WGCNA) to identify hub genes of mature skin and hair follicles in Inner Mongolian cashmere goats. Methods We used transcriptome sequencing data for the skin of Inner Mongolian cashmere goats from fetal days 45–135 days, and divided the co expressed genes into different modules by WGCNA. Characteristic values were used to screen out modules that wer

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Wijayanto, A. W., and A. Pindarwati. "Effective Graph Protection Method to Prevent the Spreading of Attacks in Networks." Indonesian Journal of Computing, Engineering and Design (IJoCED) 1, no. 2 (2019): 77. http://dx.doi.org/10.35806/ijoced.v1i2.61.

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Networks are fundamental models for representing and analyzing the structures of real-world systems. For instance, in social networks, nodes are used to represent users and edges represent the connection between users. Networks are also termed as graphs in the discrete mathematics language. One essential problem in networks is how to protect a limited number of nodes to prevent the spreading of malicious attacks or dangerous rumor in the networks, which is known as the graph protection problem. In this paper, an effective graph protection method called PowerShield is proposed which pre-emptive

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Zayed, E. M. E., та I. H. Abdel-Halim. "The wave equation approach to an inverse eigenvalue problem for an arbitrary multiply connected drum inℝ2with Robin boundary conditions". International Journal of Mathematics and Mathematical Sciences 25, № 11 (2001): 717–26. http://dx.doi.org/10.1155/s0161171201005300.

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The spectral functionμˆ(t)=∑j=1∞exp(−itμj1/2), where{μj}j=1∞are the eigenvalues of the two-dimensional negative Laplacian, is studied for small|t|for a variety of domains, where−∞<t<∞andi=−1. The dependencies ofμˆ(t)on the connectivity of a domain and the Robin boundary conditions are analyzed. Particular attention is given to an arbitrary multiply-connected drum inℝ2together with Robin boundary conditions on its boundaries.

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Xu, Mingye, Zhipeng Zhou, and Yu Qiao. "Geometry Sharing Network for 3D Point Cloud Classification and Segmentation." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 07 (2020): 12500–12507. http://dx.doi.org/10.1609/aaai.v34i07.6938.

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In spite of the recent progresses on classifying 3D point cloud with deep CNNs, large geometric transformations like rotation and translation remain challenging problem and harm the final classification performance. To address this challenge, we propose Geometry Sharing Network (GS-Net) which effectively learns point descriptors with holistic context to enhance the robustness to geometric transformations. Compared with previous 3D point CNNs which perform convolution on nearby points, GS-Net can aggregate point features in a more global way. Specially, GS-Net consists of Geometry Similarity Co

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VOLTA, ANTONIO, MIRCEA GALICEANU, AUREL JURJIU, TOMMASO GALLO, and LUCIANO GUALANDRI. "DYNAMICS ON MULTILAYERED HYPERBRANCHED FRACTALS THROUGH CONTINUOUS TIME RANDOM WALKS." Modern Physics Letters B 26, no. 09 (2012): 1250055. http://dx.doi.org/10.1142/s0217984912500558.

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We introduce a new method to generate three-dimensional structures, with mixed topologies. We focus on Multilayered Regular Hyperbranched Fractals (MRHF), three-dimensional networks constructed as a set of identical generalized Vicsek fractals, known as Regular Hyperbranched Fractals (RHF), layered on top of each other. Every node of any layer is directly connected only to copies of itself from nearest-neighbor layers. We found out that also for MRHF the eigenvalue spectrum of the connectivity matrix is determined through a semi-analytical method, which gives the opportunity to analyze very la

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