Article
Mathematics
Kaiyang Lan, Jianxi Li, Feng Liu
Summary: This paper studies the relationship between the largest eigenvalue and the balanced clique number of signed graphs, and provides extremal characteristics reaching the upper bounds. Additionally, the paper explores the impact of removing a vertex on the largest eigenvalue.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2023)
Article
Mathematics, Applied
Xiaona Fang, Lihua You, Yufei Huang
Summary: This paper characterizes the maximal graphs with the bipartite graph K-2, K-s as a star complement for eigenvalues mu = -2, 1, and explores other eigenvalues for future research.
Article
Mathematics, Applied
Jie Xue, Ruifang Liu, Jinlong Shu
Summary: This paper discusses the distance eigenvalues of chain graphs and characterizes all connected graphs with a third largest distance eigenvalue of at most -1 using clique extension. It also proves that a graph is determined by its distance spectrum if its third largest distance eigenvalue is less than -1.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Jae Young Yang, Jack H. Koolen
Summary: This paper proves that for a fixed lambda value, there exists a range of the maximum number of vertices of a connected k-regular graph with second largest eigenvalue at most lambda when k exceeds a certain threshold.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics, Applied
Liang Wei, Faxu Li, Haixing Zhao, Bo Deng
Summary: A new method for characterizing the controllability of graphs with diameter n-2 is presented, along with a necessary and sufficient condition for determining non-main eigenvalues. The visualization representation of statistical results shows that the proportion of controllable graphs among the graphs with diameter n-2 is stable at 15%, partially verifying a conjecture proposed by Stanić.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Computer Science, Artificial Intelligence
Muhammad Imran, Yasir Ali, Mehar Ali Malik, Kiran Hasnat
Summary: This paper investigates the chromatic spectrum of three different classes of 2-regular bipartite colored graphs and proves that the nullity of G is not the sum of nullities of components of G in these classes. Furthermore, important properties and conjectures are highlighted to extend this problem to general graphs.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2021)
Article
Mathematics
Guantao Chen, Yanli Hao
Summary: In this paper, upper bounds on the multiplicity of the second-largest eigenvalue of the adjacency matrix are established for 3-connected planar graphs and 2-connected outerplanar graphs. It is shown that these bounds are optimal for connected planar and outerplanar graphs.
JOURNAL OF GRAPH THEORY
(2021)
Article
Mathematics
Denis Borisov
Summary: The paper explores a general second order self-adjoint elliptic operator on an arbitrary metric graph with a glued small graph. By introducing a special operator and assuming no embedded eigenvalues, it is proven that the spectrum of the perturbed operator converges to that of the limiting operator, along with the convergence of the spectral projectors. Additionally, it is shown that the eigenvalues and eigenfunctions of the perturbed operator converging to limiting discrete eigenvalues are analytic in epsilon.
Article
Mathematics, Applied
Shuchao Li, Wanting Sun
Summary: In 2021, Liu, Chen, and Stanic determined all connected graphs that are free of {K-1, K-3, K-5-e} and have a second largest eigenvalue lambda(2) <= 1. This paper identifies all connected outerplanar graphs that are free of {K-2, K-3, K-4} and have a second largest eigenvalue not exceeding 1. Furthermore, the result obtained in this paper can be used to deduce all maximal outerplanar graphs with the same property by analyzing the local structure of the outerplanar graph with respect to its girth.
RESULTS IN MATHEMATICS
(2023)
Article
Mathematics, Applied
Yanni Dong, Shengning Qiao, Bing Chen, Pengfei Wan, Shenggui Zhang
Summary: The study focuses on the properties of degree-based entropy in bipartite graphs and trees. The maximum degree-based entropy among bipartite graphs and trees is obtained by characterizing corresponding degree sequences.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics
Juergen Jost, Raffaella Mulas, Florentin Muench
Summary: The passage discusses a new method for proving the maximum eigenvalue of a normalized graph Laplacian, as well as a lower bound on the largest eigenvalue based on the minimum vertex degree, while also specifying the conditions for equality in these cases.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2022)
Article
Mathematics
Shu-Guang Guo, Rong Zhang
Summary: The paper studies the eigenvalue properties of the A(α) matrix of a simple undirected graph G, obtaining comparison results for the largest and smallest eigenvalues.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics, Applied
Mustapha Aouchiche, Issmail El Hallaoui
Summary: In this paper, the minimum values of the second largest signless Laplacian eigenvalue of a connected graph G are investigated. The five smallest values of q(2)(G) over the set of connected graphs G with given order n are found. The extremal graphs corresponding to these values are characterized.
DISCRETE APPLIED MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Yan Sun, Haixing Zhao
Summary: Graph entropy is an important measure of network evolution and complexity, especially for bipartite graphs. In this study, the eigenvalue-based entropy of directed bipartite networks was defined, showing that networks with high entropy values tend to be disorderly while those with low entropy values tend to be regular. The experimental results on real-world directed movie recommendation networks demonstrate the validity of eigenvalue-based entropy in analyzing directed bipartite networks.
COMPLEX & INTELLIGENT SYSTEMS
(2022)
Article
Mathematics
Sasmita Barik, Subhasish Behera
Summary: This article studies some properties of unicyclic graphs. Firstly, it provides some unicyclic graphs that satisfy certain conditions. Then, it identifies the graph with the maximum eigenvalue among graphs that meet specific conditions. Finally, it proves that a specific graph has the maximum eigenvalue among all unicyclic graphs. Through these studies, a sharp upper bound for the eigenvalue of unicyclic graphs is obtained.
LINEAR & MULTILINEAR ALGEBRA
(2023)
Article
Medicine, General & Internal
Danijela M. Cvetkovic, Bojan Z. Milosevic, Aleksandar M. Cvetkovic, Srdjan M. Ninkovic, Jovana Jovankic, Dalibor Jovanovic, Snezana D. Markovic
VOJNOSANITETSKI PREGLED
(2019)
Article
Orthopedics
Jelena Zvekic-Svorcan, Jelena Aleksic, Tanja Jankovic, Karmela Filipovic, Milan Cvetkovic, Miljanka Vuksanovic, Predrag Filipov
JOURNAL OF BACK AND MUSCULOSKELETAL REHABILITATION
(2019)
Article
Telecommunications
Nenad D. Milosevic, Jelena A. Anastasov, Aleksandra M. Cvetkovic, Daniela M. Milovic, Dejan N. Milic
WIRELESS PERSONAL COMMUNICATIONS
(2019)
Article
Transplantation
Evgenia Preka, Marjolein Bonthuis, Jerome Harambat, Kitty J. Jager, Jaap W. Groothoff, Sergey Baiko, Aysun K. Bayazit, Michael Boehm, Mirjana Cvetkovic, Vidar O. Edvardsson, Svitlana Fomina, James G. Heaf, Tuula Holtta, Eva Kis, Gabriel Kolvek, Linda Koster-Kamphuis, Elena A. Molchanova, Marina Munoz, Gisela Neto, Gregor Novljan, Nikoleta Printza, Emilija Sahpazova, Lisa Sartz, Manish D. Sinha, Enrico Vidal, Karel Vondrak, Isabelle Vrillon, Lutz T. Weber, Marcus Weitz, Ilona Zagozdzon, Constantinos J. Stefanidis, Sevcan A. Bakkaloglu
NEPHROLOGY DIALYSIS TRANSPLANTATION
(2019)
Article
Biotechnology & Applied Microbiology
Alice Ferreira, Belina Ribeiro, Ana F. Ferreira, Marileide L. A. Tavares, Jelena Vladic, Senka Vidovic, Dragoljub Cvetkovic, Lusine Melkonyan, Gayane Avetisova, Vigen Goginyan, Luisa Gouveia
BIOFUELS BIOPRODUCTS & BIOREFINING-BIOFPR
(2019)
Article
Medicine, General & Internal
Zorica Dimitrijevic, Andriana Jovanovic, Mina Cvetkovic, Tamara Vrecic, Emina Kostic, Branka Mitic
MEDICINA-LITHUANIA
(2019)
Article
Toxicology
Danijela D. Nikodijevic, Milena G. Milutinovic, Danijela M. Cvetkovic, Maja D. Cupurdija, Milena M. Jovanovic, Ivan Mrkic, Marija D. Jankulovic-Gavrovic, Snezana D. Markovic
Summary: This study suggests that bee venom and its dominant compound melittin have anticancer properties against colorectal carcinoma cells by inducing proapoptotic activity and suppressing genes involved in biotransformation process. They also show selectivity against cancer cells compared to normal cells, indicating potential for developing resistance in colorectal cancer cells.
Article
Chemistry, Analytical
Marko M. Cvetkovic, Denise Soares, Joao Santos Baptista
Summary: This study analyzes the discomfort developed during long driving periods by examining modified preferred postures, pressure at the interface with the seat, and changes in pre- and post-driving gait patterns. The study found that pressure at the interface increased over time, leading to local or whole-body discomfort for drivers. Drivers try to compensate for this discomfort by modifying their posture, and changes in gait patterns can be observed after long steering periods.
Article
Chemistry, Multidisciplinary
Mojtaba Mirakhorlo, Nick Kluft, Raj Desai, Marko Cvetkovic, Tugrul Irmak, Barys Shyrokau, Riender Happee
Summary: This paper presents the validation of a multi-segment full-body human model for postural stabilization in dynamic driving. The model matches human motion and reproduces oscillations in different directions. The study shows the importance of visuo-vestibular and muscle spindle feedback for head-neck stabilization and active leg muscle control for trunk stabilization. Human modeling can accelerate the innovation of seats and vehicle motion-control strategies.
APPLIED SCIENCES-BASEL
(2022)
Proceedings Paper
Automation & Control Systems
Marko Cvetkovic, Denise Soares, Pedro Fonseca, Sara Ferreira, J. Santos Baptista
OCCUPATIONAL AND ENVIRONMENTAL SAFETY AND HEALTH II
(2020)
Proceedings Paper
Energy & Fuels
Digvijay Gusain, Milos Cvetkovic, Peter Palensky
2019 IEEE MILAN POWERTECH
(2019)
Proceedings Paper
Computer Science, Hardware & Architecture
Anna Susnjara, Jure Ravnik, Ozbej Verhnjak, Dragan Poljak, Mario Cvetkovic
2019 27TH INTERNATIONAL CONFERENCE ON SOFTWARE, TELECOMMUNICATIONS AND COMPUTER NETWORKS (SOFTCOM)
(2019)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Dragan Poljak, Mario Cvetkovic
2019 4TH INTERNATIONAL CONFERENCE ON SMART AND SUSTAINABLE TECHNOLOGIES (SPLITECH)
(2019)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Jure Ravnik, A. Susnjara, Jan Tibuat, Dragan Poljak, M. Cvetkovic
2019 4TH INTERNATIONAL CONFERENCE ON SMART AND SUSTAINABLE TECHNOLOGIES (SPLITECH)
(2019)
Proceedings Paper
Engineering, Electrical & Electronic
Claudio David Lopez, Milos Cvetkovic, Peter Palensky
2019 IEEE 28TH INTERNATIONAL SYMPOSIUM ON INDUSTRIAL ELECTRONICS (ISIE)
(2019)
Article
Mathematics, Applied
Muhammad Syifa'ul Mufid, Ebrahim Patel, Sergei Sergeev
Summary: This paper presents an approach to solve maxmin-omega linear systems by performing normalization and generating a principal order matrix. The possible solution indices can be identified using the principal order matrix and the parameter omega, and the fully active solutions can be obtained from these indices. Other solutions can be found by applying a relaxation to the fully active solutions. This approach can be seen as a generalization of solving max-plus or min-plus linear systems. The paper also highlights the unusual feature of maxmin-omega linear systems having a finite number of solutions when the solution is non-unique.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
E. Mainar, J. M. Pena, B. Rubio
Summary: A bidiagonal decomposition of quantum Hilbert matrices is obtained and the total positivity of these matrices is proved. This factorization is used for accurate algebraic computations and the numerical errors caused by imprecise computer arithmetic or perturbed input data are analyzed. Numerical experiments demonstrate the accuracy of the proposed methods.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhong-Zhi Bai
Summary: This study explores the algebraic structures and computational properties of Wasserstein-1 metric matrices. It shows that these matrices can be expressed using the Neumann series of nilpotent matrices and can be accurately and stably computed by solving unit bidiagonal triangular systems of linear equations.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Bogdan Nica
Summary: This study investigates the relationship between the independence number and chromatic number in a graph of non-singular matrices over a finite field, and obtains an upper bound for the former and a lower bound for the latter.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Dijian Wang, Yaoping Hou, Deqiong Li
Summary: In this paper, a Turán-like problem in signed graphs is studied. The properties of signed graphs are proven in the context of the problem.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Tyler Chen, Thomas Trogdon
Summary: This study focuses on the stability of the Lanczos algorithm when applied to problems with eigenvector empirical spectral distribution close to a reference measure characterized by well-behaved orthogonal polynomials. The analysis reveals that the Lanczos algorithm is forward stable on many large random matrix models, even in finite precision arithmetic, which indicates that random matrices differ significantly from general matrices and caution must be exercised when using them to test numerical algorithms.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Constantin Costara
Summary: This passage discusses linear mappings on matrices and the relationship between subsets of the spectrum, providing corresponding characterization conditions.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Amir Hossein Ghodrati, Mohammad Ali Hosseinzadeh
Summary: This paper presents tight upper bounds for all signless Laplacian eigenvalues of a graph with prescribed order and minimum degree, improving upon previously known bounds. Additionally, the relationship between the number of signless Laplacian eigenvalues falling within specific intervals and various graph parameters such as independence, clique, chromatic, edge covering, and matching numbers is explored.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Ya-Lei Jin, Jie Zhang, Xiao-Dong Zhang
Summary: This paper investigates the relationship between the spectral radius of a symmetric matrix and its principal submatrices, and uses these relationships to obtain upper bounds of the spectral radius of graphs.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Davide Bolognini, Paolo Sentinelli
Summary: We introduce immanant varieties associated with simple characters of a finite group and discuss the features of one-dimensional characters and trivial characters.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
A. S. Gordienko
Summary: We introduce the concept of a graded group action on a graded algebra, or equivalently, a group action by graded pseudoautomorphisms. We study the properties of groups of graded pseudoautomorphisms and prove several important theorems and conjectures regarding graded algebras with a group action.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Jiaqi Gu, Shenghao Feng, Yimin Wei
Summary: We propose a tensor product structure compatible with the hypergraph structure and define the algebraic connectivity of the hypergraph in this product, establishing its relationship with vertex connectivity. We introduce connectivity optimization problems into the hypergraph and solve them using algebraic connectivity. Additionally, we apply the Laplacian eigenmap algorithm to the hypergraph under our tensor product.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Samuel Lichtenberg, Abiy Tasissa
Summary: This paper explores a dual basis approach to Classical Multidimensional Scaling (CMDS) and provides explicit formulas for the dual basis vectors. It also characterizes the spectrum of an essential matrix in the dual basis framework. Connections to a related problem in metric nearness are made.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2024)
