Results 11 to 20 of about 232,087 (312)

A Few Examples and Counterexamples in Spectral Graph Theory

Discussiones Mathematicae Graph Theory, 2020
We present a small collection of examples and counterexamples for selected problems, mostly in spectral graph theory, that have occupied our minds over a number of years without being completely resolved.
Stevanović Dragan, Milosavljević Nikola, Vukičević Damir   +2 more
doaj   +2 more sources

Geometric spectral theory of quantum graphs [PDF]

Communications in Mathematics
These are lecture notes from a course given at the summer school "Heat kernels and spectral geometry: from manifolds to graphs" in Bregenz, Austria, 2022. They are designed to be accessible to doctoral level students, and include background chapters on Laplacians on domains and quantum graphs before moving on to specialised topics involving the ...
James B. Kennedy
openalex   +3 more sources

Re-imagining Spectral Graph Theory [PDF]

We propose a Laplacian based on general inner product spaces, which we call the inner product Laplacian. We show the combinatorial and normalized graph Laplacians, as well as other Laplacians for hypergraphs and directed graphs, are special cases of the inner product Laplacian. After developing the necessary basic theory for the inner product Laplacian,
Sinan G. Aksoy, Stephen J. Young
openalex   +3 more sources

SPectral graph theory And Random walK (SPARK) toolbox for static and dynamic characterization of (di)graphs: A tutorial. [PDF]

PLoS One
Ranieri A, Pichiorri F, Colamarino E, Cincotti F, Mattia D, Toppi J.   +5 more
europepmc   +2 more sources

Algorithm Design Using Spectral Graph Theory

, 2013
Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. Laplace’s equation and its discrete form, the Laplacian matrix, appear ubiquitously in mathematical physics. Due to the recent discovery of very fast solvers for these equations, they are also becoming increasingly useful in combinatorial optimization ...
Richard Peng
openalex   +3 more sources

Spectral graph theory

, 2010
Dragoš Cvetković, Peter Rowlinson
openalex   +2 more sources

Spectral Graph Theory: Eigen Values Laplacians and Graph Connectivity

Metallurgical and Materials Engineering
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.
Jitender Kumar, B. Archana, Ramya Muralidharan   +2 more
openalex   +3 more sources

Spectral Integral Variation of Graph Theory

Asian Journal of Mathematics and Computer Research
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 ...
Hawa Ahmed Alrawayati, Ümit Tokeşer
openalex   +3 more sources

Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms. [PDF]

Philos Trans A Math Phys Eng Sci
Minenkova A, Mograby G, Zhan H.
europepmc   +2 more sources

On the spectral radius of VDB graph matrices

Vojnotehnički Glasnik, 2023
Introduction/purpose: Vertex-degree-based (VDB) graph matrices form a special class of matrices, corresponding to the currently much investigated vertex-degree-based (VDB) graph invariants. Some spectral properties of these matrices are investigated.
Ivan Gutman
doaj   +1 more source