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Journal articles on the topic 'Spectral graph theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Cvetkovic, Dragos. "Spectral recognition of graphs." Yugoslav Journal of Operations Research 22, no. 2 (2012): 145–61. http://dx.doi.org/10.2298/yjor120925025c.

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At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra. Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs) were found. Still some graphs are characterized by their spectra and several mathematical papers are devoted to this topic. In applications to computer sciences, spectral graph theory is considered as very strong. The benefit of using graph spectra in treating graphs is that

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2

Alrawayati, Hawa Ahmed, and Ümit Tokeşer. "Spectral Integral Variation of Graph Theory." Asian Journal of Mathematics and Computer Research 32, no. 2 (2025): 151–60. https://doi.org/10.56557/ajomcor/2025/v32i29173.

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Spectral integral variation in graph theory explores the interplay between the spectral properties of graphs and their topological and geometrical characteristics. This study focuses on the eigenvalues and eigenvectors of graph-related matrices, such as the adjacency matrix and the Laplacian matrix, and their implications for understanding graph structure, connectivity, and dynamics. By examining integral variations, we establish a framework for analyzing how spectral properties change under perturbations, such as edge weight modifications and graph transformations. This paper discusses the si

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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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4

Cvetkovic, Dragos, and Slobodan Simic. "Towards a spectral theory of graphs based on the signless Laplacian, I." Publications de l'Institut Math?matique (Belgrade) 85, no. 99 (2009): 19–33. http://dx.doi.org/10.2298/pim0999019c.

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A spectral graph theory is a theory in which graphs are studied by means of eigenvalues of a matrix M which is in a prescribed way defined for any graph. This theory is called M-theory. We outline a spectral theory of graphs based on the signless Laplacians Q and compare it with other spectral theories, in particular with those based on the adjacency matrix A and the Laplacian L. The Q-theory can be composed using various connections to other theories: equivalency with A-theory and L-theory for regular graphs, or with L-theory for bipartite graphs, general analogies with A-theory and analogies

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Hayat, Sakander, Asad Khan, and Mohammed J. F. Alenazi. "On Some Distance Spectral Characteristics of Trees." Axioms 13, no. 8 (2024): 494. http://dx.doi.org/10.3390/axioms13080494.

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Graham and Pollack in 1971 presented applications of eigenvalues of the distance matrix in addressing problems in data communication systems. Spectral graph theory employs tools from linear algebra to retrieve the properties of a graph from the spectrum of graph-theoretic matrices. The study of graphs with “few eigenvalues” is a contemporary problem in spectral graph theory. This paper studies graphs with few distinct distance eigenvalues. After mentioning the classification of graphs with one and two distinct distance eigenvalues, we mainly focus on graphs with three distinct distance eigenva

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Hammond, David K., Pierre Vandergheynst, and Rémi Gribonval. "Wavelets on graphs via spectral graph theory." Applied and Computational Harmonic Analysis 30, no. 2 (2011): 129–50. http://dx.doi.org/10.1016/j.acha.2010.04.005.

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7

Jin, Ming, Heng Chang, Wenwu Zhu, and Somayeh Sojoudi. "Power up! Robust Graph Convolutional Network via Graph Powering." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (2021): 8004–12. http://dx.doi.org/10.1609/aaai.v35i9.16976.

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Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be vulnerable to topological attacks. To enhance adversarial robustness, we go beyond spectral graph theory to robust graph theory. By challenging the classical graph Laplacian, we propose a new convolution operator that is provably robust in the spectral domain and is incorporated in the GCN architecture to improve expressivity and interpretability. By extending the original graph to a sequence of graphs, we also propose a robust training paradigm that encourages transfe

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Sason, Igal, Noam Krupnik, Suleiman Hamud, and Abraham Berman. "On Spectral Graph Determination." Mathematics 13, no. 4 (2025): 549. https://doi.org/10.3390/math13040549.

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The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods to construct or distinguish cospectral nonisomorphic graphs, and analyzing the conditions under which a graph’s spectrum uniquely determines its structure. This paper presents an overview of both classical and recent advancements in these topics, along with newly obtained proofs of some existing results, which offer additional insights.

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Abdian, Ali Zeydi, and S. Morteza Mirafzal. "The spectral characterizations of the connected multicone graphs Kw ▽ LHS and Kw ▽ LGQ(3,9)." Discrete Mathematics, Algorithms and Applications 10, no. 02 (2018): 1850019. http://dx.doi.org/10.1142/s1793830918500192.

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In the past decades, graphs that are determined by their spectrum have received much more and more attention, since they have been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning. An important part of spectral graph theory is devoted to determining whether given graphs or classes of graphs are determined by their spectra or not. So, finding and introducing any class of graphs which are determined by their spectra can be an interesting and important problem. The main aim of this study is to characterize two classes of multicone

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Yu, Guidong, Tao Yu, Xiangwei Xia, and Huan Xu. "Spectral Sufficient Conditions on Pancyclic Graphs." Complexity 2021 (July 15, 2021): 1–8. http://dx.doi.org/10.1155/2021/3630245.

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A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n . In fact, it is NP-complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to be pancyclic in terms of the spectral radius and the signless Laplacian spectral radius of the graph.

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J. Satish Kumar, B. Archana, and K. Muralidharan, R. Srija. "Spectral Graph Theory: Eigen Values Laplacians and Graph Connectivity." Metallurgical and Materials Engineering 31, no. 3 (2025): 78–84. https://doi.org/10.63278/1321.

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Spectral graph theory investigates how graph structures and specific matrix eigenvalues of adjacency matrices and Laplacian matrices relate to each other. The following paper explains fundamental spectral graph theory concepts by analyzing eigenvalues alongside Laplacians which help evaluate graph connectivity. The spectral characteristics of these matrices provide crucial insights into the graph structure that include properties regarding connectivity as well as expansion features and operational reliability. The paper explains essential theorems alongside applications and methodology of spec

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12

Lurie, Jacob. "Review of Spectral Graph Theory." ACM SIGACT News 30, no. 2 (1999): 14–16. http://dx.doi.org/10.1145/568547.568553.

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13

Nivetha, P. "Spectral Graph Theory and Its Applications in Image Processing and Computer Vision." International Journal for Research in Applied Science and Engineering Technology 13, no. 6 (2025): 330–35. https://doi.org/10.22214/ijraset.2025.71982.

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Spectral Graph Theory provides a powerful mathematical framework to study graphs using the spectral (eigenvalue and eigenvector) properties of matrices associated with them, such as the adjacency matrix and Laplacian matrix. In image processing and computer vision, images are often modeled as graphs to capture spatial and structural relationships between pixels or regions. This paper explores the foundational concepts of spectral graph theory and its pivotal role in various image analysis tasks, including segmentation, denoising, object recognition, and 3D shape analysis. Applications are supp

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Cui, Yaqi, Yuanyuan Chen, Dan Li, and Yue Zhang. "Domination number and (signless Laplacian) spectral radius of cactus graphs." Electronic Journal of Linear Algebra 41 (April 30, 2025): 277–87. https://doi.org/10.13001/ela.2025.9307.

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A cactus graph is a connected graph whose block is either an edge or a cycle. A vertex set $S\subseteq V(G)$ is said to be a dominating set of a graph $G$ if every vertex in $V(G)\setminus S$ is adjacent to a vertex in $S$. There are several results on the (signless Laplacian) spectral radius and domination number in graph theory. In this paper, we determine the unique graph with the maximum adjacency spectral radius and signless Laplacian spectral radius among all cactus graphs with fixed domination number.

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Li, Dan, Guoping Wang, and Jixiang Meng. "On the distance signless Laplacian spectral radius of graphs and digraphs." Electronic Journal of Linear Algebra 32 (February 6, 2017): 438–46. http://dx.doi.org/10.13001/1081-3810.1982.

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Let \eta(G) denote the distance signless Laplacian spectral radius of a connected graph G. In this paper,bounds for the distance signless Laplacian spectral radius of connected graphs are given, and the extremal graph with the minimal distance signless Laplacian spectral radius among the graphs with given vertex connectivity and minimum degree is determined. Furthermore, the digraph that minimizes the distance signless Laplacian spectral radius with given vertex connectivity is characterized.

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Pardo-Guerra, Sebastian, Vivek Kurien George, Vikash Morar, Joshua Roldan, and Gabriel Alex Silva. "Extending Undirected Graph Techniques to Directed Graphs via Category Theory." Mathematics 12, no. 9 (2024): 1357. http://dx.doi.org/10.3390/math12091357.

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We use Category Theory to construct a ‘bridge’ relating directed graphs with undirected graphs, such that the notion of direction is preserved. Specifically, we provide an isomorphism between the category of simple directed graphs and a category we call ‘prime graphs category’; this has as objects labeled undirected bipartite graphs (which we call prime graphs), and as morphisms undirected graph morphisms that preserve the labeling (which we call prime graph morphisms). This theoretical bridge allows us to extend undirected graph techniques to directed graphs by converting the directed graphs

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17

Goh, Hung Lik, Wan Heng Fong, and Sherzod Turaev. "Spectral Bipartition via Gap Cut on DNA Sequences." Semarak International Journal of Fundamental and Applied Mathematics 3, no. 1 (2024): 11–27. http://dx.doi.org/10.37934/sijfam.3.1.1127.

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Deoxyribonucleic Acid (DNA) and graph partitioning are two distinct fields of study which can be linked in the structure of biological networks. Graph partitioning has been extensively studied but not its application in the biological field. This research explored on the application of spectral graph partitioning in DNA splicing, aiming to simulate the cleavage of DNA by performing spectral bipartition on DNA sequences in a DNA splicing system. This research incorporates Fiedler theory and algebraic graph theory, which are commonly utilized in network analysis and the analysis of graph connect

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18

Yamada, Hiroshi. "Geary’s c and Spectral Graph Theory." Mathematics 9, no. 19 (2021): 2465. http://dx.doi.org/10.3390/math9192465.

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Spatial autocorrelation, of which Geary’s c has traditionally been a popular measure, is fundamental to spatial science. This paper provides a new perspective on Geary’s c. We discuss this using concepts from spectral graph theory/linear algebraic graph theory. More precisely, we provide three types of representations for it: (a) graph Laplacian representation, (b) graph Fourier transform representation, and (c) Pearson’s correlation coefficient representation. Subsequently, we illustrate that the spatial autocorrelation measured by Geary’s c is positive (resp. negative) if spatially smoother

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Adiga, Chandrashekar, Kinkar Das, and B. R. Rakshith. "Some Graphs Determined by their Signless Laplacian (Distance) Spectra." Electronic Journal of Linear Algebra 36, no. 36 (2020): 461–72. http://dx.doi.org/10.13001/ela.2020.4951.

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In literature, there are some results known about spectral determination of graphs with many edges. In [M.~C\'{a}mara and W.H.~Haemers. Spectral characterizations of almost complete graphs. {\em Discrete Appl. Math.}, 176:19--23, 2014.], C\'amara and Haemers studied complete graph with some edges deleted for spectral determination. In fact, they found that if the deleted edges form a matching, a complete graph $K_m$ provided $m \le n-2$, or a complete bipartite graph, then it is determined by its adjacency spectrum. In this paper, the graph $K_{n}\backslash K_{l,m}$ $(n>l+m)$ which is obtai

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20

Granziol, Diego, Binxin Ru, Xiaowen Dong, Stefan Zohren, Michael Osborne, and Stephen Roberts. "Maximum Entropy Approach to Massive Graph Spectrum Learning with Applications." Algorithms 15, no. 6 (2022): 209. http://dx.doi.org/10.3390/a15060209.

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We propose an alternative maximum entropy approach to learning the spectra of massive graphs. In contrast to state-of-the-art Lanczos algorithm for spectral density estimation and applications thereof, our approach does not require kernel smoothing. As the choice of kernel function and associated bandwidth heavily affect the resulting output, our approach mitigates these issues. Furthermore, we prove that kernel smoothing biases the moments of the spectral density. Our approach can be seen as an information-theoretically optimal approach to learning a smooth graph spectral density, which fully

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21

Kaliuzhnyi-Verbovetskyi, D., and V. Pivovarchik. "RECOVERING THE SHAPE OF A QUANTUM CATERPILLAR TREE BY TWO SPECTRA." Mechanics And Mathematical Methods 5, no. 1 (2023): 14–24. http://dx.doi.org/10.31650/2618-0650-2023-5-1-14-24.

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existence of co-spectral (iso-spectral) graphs is a well-known problem of the classical graph theory. However, co-spectral graphs exist in the theory of quantum graphs also. In other words, the spectrum of the Sturm-Liouville problem on a metric graph does not determine alone the shape of the graph. Сo-spectral trees also exist if the number of vertices exceeds eight. We consider two Sturm-Liouville spectral problems on an equilateral metric caterpillar tree with real L2 (0,l) potentials on the edges. In the first (Neumann) problem we impose standard conditions at all vertices: Neumann boundar

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Zhao, Jietong, Saira Hameed, Uzma Ahmad, Ayesha Tabassum, and Leila Asgharsharghi. "Sequence of Bounds for Spectral Radius and Energy of Digraph." Symmetry 16, no. 10 (2024): 1386. http://dx.doi.org/10.3390/sym16101386.

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The graph spectra analyze the structure of the graph using eigenspectra. The spectral graph theory deals with the investigation of graphs in terms of the eigenspectrum. In this paper, the sequence of lower bounds for the spectral radius of digraph D having at least one doubly adjacent vertex in terms of indegree is proposed. Particularly, it is exhibited that ρ(D)≥αj=∑p=1m(χj+1(p))2∑p=1m(χj(p))2, such that equality is attained iff D=G↔+ {DE∉ Cycle}, where each component of associated graph is a k-regular or (k1,k2) semiregular bipartite. By utilizing the sequence of lower bounds of the spectra

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23

NATH, MILAN, and SOMNATH PAUL. "GRAPH TRANSFORMATION AND DISTANCE SPECTRAL RADIUS." Discrete Mathematics, Algorithms and Applications 05, no. 03 (2013): 1350014. http://dx.doi.org/10.1142/s1793830913500146.

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Trees are very common in the theory and applications of combinatorics. In this paper, we consider graphs whose underlying structure is a tree and study the behavior of the distance spectral radius under a graph transformation. As an application, we find the corona tree that maximizes the distance spectral radius among all corona trees with a fixed maximum degree. We also find the graph with minimal (maximal) distance spectral radius among all corona trees. Finally, we determine the graph with minimal distance spectral radius in a special class of corona trees.

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Yurttas Gunes, Aysun, Muge Togan, Musa Demirci, and Ismail Naci Cangul. "Harmonic Index and Zagreb Indices of Vertex-Semitotal Graphs." European Journal of Pure and Applied Mathematics 13, no. 5 (2020): 1260–69. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3725.

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Graph theory is one of the rising areas in mathematics due to its applications in many areas of science. Amongst several study areas in graph theory, spectral graph theory and topological descriptors are in front rows. These descriptors are widely used in QSPR/QSAR studies in mathematical chemistry. Vertex-semitotal graphs are one of the derived graph classes which are useful in calculating several physico-chemical properties of molecular structures by means of molecular graphs modelling the molecules. In this paper, several topological descriptors of vertex-semitotal graphs are calculated. So

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Kumar, Pawan, Siddique Merajuddin, Shariefuddin Pirzada, and Yilun Shang. "On the Spectral Redundancy of Pineapple Graphs." Symmetry 16, no. 10 (2024): 1267. http://dx.doi.org/10.3390/sym16101267.

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In this article, we explore the concept of spectral redundancy within the class of pineapple graphs, denoted as P(α,β). These graphs are constructed by attaching β pendent edges to a single vertex of a complete graph Kα. A connected graph G earns the title of being spectrally non-redundant if the spectral radii of its connected induced subgraphs are all distinct. Spectral redundancy, on the other hand, arises when there is a repetition of spectral radii among the connected induced subgraphs within G. Our study analyzes the adjacency spectrum of P(α,β), identifying distinct eigenvalues such as

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Paul, Somnath. "On distance and distance Laplacian spectra of corona of two graphs." Discrete Mathematics, Algorithms and Applications 08, no. 01 (2016): 1650007. http://dx.doi.org/10.1142/s1793830916500075.

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Corona of two graphs has been defined in [F. Harary, Graph Theory (Addison-Wesley, 1969)]. In this paper, we study the distance and the distance Laplacian spectra of corona of two graphs and describe the complete distance (distance Laplacian) spectrum for some particular cases. As an application, we show that the corona operation can be used to create distance singular graphs. We also show that these results enable us to construct infinitely many pairs of distance (respectively, distance Laplacian) cospectral graphs. Last, we give a graph transformation and discuss its effect on the distance L

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Horn, Paul, Adam Purcilly, and Alex Stevens. "Graph curvature and local discrepancy." Journal of Graph Theory 108, no. 2 (2024): 337–60. https://doi.org/10.1002/jgt.23176.

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AbstractIn recent years, discrete notions of curvature have been defined and exploited to understand various geometric properties of graphs; especially regarding heat flow, and spectral properties. In this paper, we study various combinatorial properties implied by satisfying the Bakry–Émery curvature dimension inequality . In particular we derive a local discrepancy inequality, similar in spirit to the expander mixing lemma from spectral graph theory, which certifies a type of “local pseudo‐randomness” of the edge set of the graph, for graphs satisfying a curvature lower bound. In addition, s

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Coutino, Mario, Sundeep Prabhakar Chepuri, Takanori Maehara, and Geert Leus. "Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering." Algorithms 13, no. 9 (2020): 214. http://dx.doi.org/10.3390/a13090214.

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To analyze and synthesize signals on networks or graphs, Fourier theory has been extended to irregular domains, leading to a so-called graph Fourier transform. Unfortunately, different from the traditional Fourier transform, each graph exhibits a different graph Fourier transform. Therefore to analyze the graph-frequency domain properties of a graph signal, the graph Fourier modes and graph frequencies must be computed for the graph under study. Although to find these graph frequencies and modes, a computationally expensive, or even prohibitive, eigendecomposition of the graph is required, the

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Yu, Guanglong, Jianyong Wong, and Shu-guang Guo. "Maxima of the signless Laplacian spectral radius for planar graphs." Electronic Journal of Linear Algebra 30 (February 8, 2015): 795–811. http://dx.doi.org/10.13001/1081-3810.2023.

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The signless Laplacian spectral radius of a graph is the largest eigenvalue of its signless Laplacian. In this paper, we prove that the graph $K_{2}\nabla P_{n-2}$ has the maximal signless Laplacian spectral radius among all planar graphs of order $n\geq 456$.

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Liu, Fangmeng, Wei Li, and Yiwen Zhong. "A Further Study on the Degree-Corrected Spectral Clustering under Spectral Graph Theory." Symmetry 14, no. 11 (2022): 2428. http://dx.doi.org/10.3390/sym14112428.

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Spectral clustering algorithms are often used to find clusters in the community detection problem. Recently, a degree-corrected spectral clustering algorithm was proposed. However, it is only used for partitioning graphs which are generated from stochastic blockmodels. This paper studies the degree-corrected spectral clustering algorithm based on the spectral graph theory and shows that it gives a good approximation of the optimal clustering for a wide class of graphs. Moreover, we also give theoretical support for finding an appropriate degree-correction. Several numerical experiments for com

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Liu, Jia Bao. "Spectral Graph Theory in Chemical Sciences." Current Organic Synthesis 22, no. 2 (2025): vii. https://doi.org/10.2174/157017942202241030123611.

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32

LIU, XIAOGANG. "SELECTED TOPICS IN SPECTRAL GRAPH THEORY." Bulletin of the Australian Mathematical Society 93, no. 3 (2016): 511–12. http://dx.doi.org/10.1017/s0004972715001768.

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Raj, Ashish, Chang Cai, Xihe Xie, et al. "Spectral graph theory of brain oscillations." Human Brain Mapping 41, no. 11 (2020): 2980–98. http://dx.doi.org/10.1002/hbm.24991.

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Celik, Feriha, Utkum Sanli, and Ismail Naci Cangul. "The spectral polynomials of two joining graphs: splices and links." Boletim da Sociedade Paranaense de Matemática 40 (January 26, 2022): 1–12. http://dx.doi.org/10.5269/bspm.48651.

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Energy of a graph, firstly defined by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix, in other words the sum of absolute values of the roots of the characteristic (spectral) polynomials, is an important sub area of graph theory. Symmetry and regularity are two important and desired properties in many areas including graphs. In many molecular graphs, we have a pointwise symmetry, that is the graph corresponding to the molecule under investigation has two identical subgraphs which are symmetrical at a vertex. Therefore, in this paper, we shall study only the v

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Li, Yu, Meng Qu, Jian Tang, and Yi Chang. "Signed Laplacian Graph Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 4 (2023): 4444–52. http://dx.doi.org/10.1609/aaai.v37i4.25565.

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This paper studies learning meaningful node representations for signed graphs, where both positive and negative links exist. This problem has been widely studied by meticulously designing expressive signed graph neural networks, as well as capturing the structural information of the signed graph through traditional structure decomposition methods, e.g., spectral graph theory. In this paper, we propose a novel signed graph representation learning framework, called Signed Laplacian Graph Neural Network (SLGNN), which combines the advantages of both. Specifically, based on spectral graph theory a

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Triyani, Triyani, Mashuri Mashuri, Bunga Tirai Anarkis, and Slamet Riyadi. "The spectrum on prism graph using circulant matrix." Bulletin of Applied Mathematics and Mathematics Education 2, no. 1 (2022): 1–10. http://dx.doi.org/10.12928/bamme.v2i1.5129.

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Spectral graph theory discusses about the algebraic properties of graphs based on the spectrum of a graph. This article investigated the spectrum of prism graph. The method used in this research is the circulant matrix. The results showed that prism graph P2,s is a regular graph of degree 3, for s odd and s ≥ 3, P2,s is a circulantt graph with regular spectrum.

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SUNTORNPOCH, BORWORN, and YOTSANAN MEEMARK. "CAYLEY GRAPHS OVER A FINITE CHAIN RING AND GCD-GRAPHS." Bulletin of the Australian Mathematical Society 93, no. 3 (2016): 353–63. http://dx.doi.org/10.1017/s0004972715001380.

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We extend spectral graph theory from the integral circulant graphs with prime power order to a Cayley graph over a finite chain ring and determine the spectrum and energy of such graphs. Moreover, we apply the results to obtain the energy of some gcd-graphs on a quotient ring of a unique factorisation domain.

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Das, Kinkar, and SHAOWEI SUN. "Extremal graph on normalized Laplacian spectral radius and energy." Electronic Journal of Linear Algebra 29 (September 20, 2015): 237–53. http://dx.doi.org/10.13001/1081-3810.3263.

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Let $G=(V,\,E)$ be a simple graph of order $n$ and the normalized Laplacian eigenvalues $\rho_1\geq \rho_2\geq \cdots\geq\rho_{n-1}\geq \rho_n=0$. The normalized Laplacian energy (or Randi\'c energy) of $G$ without any isolated vertex is defined as $$RE(G)=\sum_{i=1}^{n}|\rho_i-1|.$$ In this paper, a lower bound on $\rho_1$ of connected graph $G$ ($G$ is not isomorphic to complete graph) is given and the extremal graphs (that is, the second minimal normalized Laplacian spectral radius of connected graphs) are characterized. Moreover, Nordhaus-Gaddum type results for $\rho_1$ are obtained. Rece

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Alrawayati, Hawa Ahmed, and Ümit Tokeşer. "Laplacian Eigenvalues of Threshold Graphs and Majorization." Asian Journal of Mathematics and Computer Research 32, no. 2 (2025): 124–34. https://doi.org/10.56557/ajomcor/2025/v32i29169.

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This paper investigates the relationship between Laplacian eigenvalues of threshold graphs and the concept of majorization. Threshold graphs, characterized by their simplicity and combinatorial properties, serve as a rich framework for exploring spectral graph theory. We analyze the Laplacian matrix of these graphs and derive conditions under which the eigenvalues exhibit majorization properties. By employing techniques from linear algebra and combinatorial optimization, we establish a set of inequalities that describe the distribution of the Laplacian eigenvalues in terms of the graph's struc

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Aydın, Büşra, Nihat Akgüneş, and İsmail Naci Cangül. "On the Wiener Index of the Dot Product Graph over Monogenic Semigroups." European Journal of Pure and Applied Mathematics 13, no. 5 (2020): 1231–40. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3745.

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Algebraic study of graphs is a relatively recent subject which arose in two main streams: One is named as the spectral graph theory and the second one deals with graphs over several algebraic structures. Topological graph indices are widely-used tools in especially molecular graph theory and mathematical chemistry due to their time and money saving applications. The Wiener index is one of these indices which is equal to the sum of distances between all pairs of vertices in a connected graph. The graph over the nite dot product of monogenic semigroups has recently been dened and in this paper,

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Kang, Ming-Hsuan, and Jing-Wen Gu. "Toroidal Spectral Drawing." Axioms 11, no. 3 (2022): 137. http://dx.doi.org/10.3390/axioms11030137.

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We give a deterministic drawing algorithm to draw a graph onto a torus, which is based on the usual spectral drawing algorithm. For most of the well-known toroidal vertex-transitive graphs, the result drawings give an embedding of the graphs onto the torus.

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42

Chen, Haiyan, and Fuji Zhang. "Spectral Dynamics of Graph Sequences Generated by Subdivision and Triangle Extension." Electronic Journal of Linear Algebra 32 (February 6, 2017): 454–63. http://dx.doi.org/10.13001/1081-3810.3583.

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For a graph G and a unary graph operation X, there is a graph sequence \G_k generated by G_0=G and G_{k+1}=X(G_k). Let Sp({G_k}) denote the set of normalized Laplacian eigenvalues of G_k. The set of limit points of \bigcup_{k=0}^\infty Sp(G_k)$, $\liminf_{k\rightarrow\infty}Sp(G_k) and $\limsup_{k\rightarrow \infty}Sp(G_k)$ are considered in this paper for graph sequences generated by two operations: subdivision and triangle extension. It is obtained that the spectral dynamic of graph sequence generated by subdivision is determined by a quadratic function, which is closely related to the the w

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43

K, SIVARANJANI, and Shanmuga Sundaram Olappalyam Vaiyapuri. "AN ANALYSIS OF THE SEIDEL LAPLACIAN ENERGY OF A FUZZY INTUITIONISTIC SYSTEM." Suranaree Journal of Science and Technology 32, no. 1 (2025): 0010350(1–14). https://doi.org/10.55766/sujst7197.

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This paper presents one of the latest research works in intuitionistic fuzzy graph theory. Along with questionable concepts conveyed in distinctive languages, intuitionistic fuzzy set theory offers a noteworthy and ground-breaking depiction of vulnerability estimation. The concept of energy is related to the spectrum of a graph. The energy of graphs plays a vital role in graph theory. In mathematics, the total sum of the absolute values of the eigenvalues of the graph’s adjacency matrix is referred to as the graph’s energy. In the framework of spectral graph theory, this quantity is extensivel

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44

Romdhini, Mamika Ujianita, Abdurahim, Andika Ellena Saufika Hakim Maharani, and Siti Raudhatul Kamali. "Transmission-Based Energies of Prime Coprime Graph for Integers Modulo Group." Science and Technology Indonesia 10, no. 3 (2025): 759–85. https://doi.org/10.26554/sti.2025.10.3.759-785.

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Graphs are an excellent instrument that provides an algebraic structure for visualizing and interpreting molecule structures and characteristics. As a result, the problem statement arises regarding how we can interpret graphs with eigenvalues concerning their corresponding matrices. Such questions can be answered by studying spectral graph theory. This research focuses on graphs whose vertex sets are group elements in which the structure of ℤn groups and the definition of a prime coprime graph serve as the foundation for the graph building used in this study. The matrix construction of the gra

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45

Romdhini, Mamika Ujianita, Abdurahim, Andika Ellena Saufika Hakim Maharani, and Siti Raudhatul Kamali. "Transmission-Based Energies of Prime Coprime Graph for Integers Modulo Group." Science and Technology Indonesia 10, no. 3 (2025): 759–65. https://doi.org/10.26554/sti.2025.10.3.759-765.

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Graphs are an excellent instrument that provides an algebraic structure for visualizing and interpreting molecule structures and characteristics. As a result, the problem statement arises regarding how we can interpret graphs with eigenvalues concerning their corresponding matrices. Such questions can be answered by studying spectral graph theory. This research focuses on graphs whose vertex sets are group elements in which the structure of ℤn groups and the definition of a prime coprime graph serve as the foundation for the graph building used in this study. The matrix construction of the gra

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46

Jog, S. R., and Raju Kotambari. "On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs." Journal of Mathematics 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/5906801.

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Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute adjacency, Laplacian, and signless Laplacian energy (Qenergy) of coalescence of pair of complete graphs. Also, as an application, we obtain the adjacency energy of subdivision graph and line graph of coalescence from itsQenergy.

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47

Simic, Slobodan, and Dragan Stevanovic. "Two shorter proofs in spectral graph theory." Publikacije Elektrotehnickog fakulteta - serija: matematika, no. 14 (2003): 94–98. http://dx.doi.org/10.2298/petf0314094s.

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Stanic, Zoran. "A game based on spectral graph theory." Publikacije Elektrotehni?kog fakulteta - serija: matematika, no. 16 (2005): 88–93. http://dx.doi.org/10.2298/petf0516088s.

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Das, Kinkar Ch, and Muhuo Liu. "On Two Conjectures of Spectral Graph Theory." Bulletin of the Iranian Mathematical Society 44, no. 1 (2018): 43–51. http://dx.doi.org/10.1007/s41980-018-0003-3.

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Simpson, Olivia. "The geometric origins of spectral graph theory." XRDS: Crossroads, The ACM Magazine for Students 21, no. 1 (2014): 15–17. http://dx.doi.org/10.1145/2667615.

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