Results 31 to 40 of about 137,715 (267)

On the A_α-Eigenvalues of Signed Graphs

Mathematics, 2021
For α∈[0,1], let Aα(Gσ)=αD(G)+(1−α)A(Gσ), where G is a simple undirected graph, D(G) is the diagonal matrix of its vertex degrees and A(Gσ) is the adjacency matrix of the signed graph Gσ whose underlying graph is G.
Germain Pastén, Oscar Rojo, Luis Medina
doaj   +1 more source

Hermitian Adjacency Matrix of Digraphs and Mixed Graphs [PDF]

Journal of Graph Theory, 2015
The article gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from x to y is equal to the complex unity i (and its ...
Krystal Guo, B. Mohar
semanticscholar   +1 more source

Aα-Spectral Characterizations of Some Joins

Journal of Mathematics, 2020
Let G be a graph with n vertices. For every real α∈0,1, write AαG for the matrix AαG=αDG+1−αAG, where AG and DG denote the adjacency matrix and the degree matrix of G, respectively.
Tingzeng Wu, Tian Zhou
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Laplacian versus adjacency matrix in quantum walk search [PDF]

Quantum Information Processing, 2015
A quantum particle evolving by Schrödinger’s equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace’s operator.
T. G. Wong, Luís Tarrataca, Nikolay Nahimov   +2 more
semanticscholar   +1 more source

Graphs Whose Aα -Spectral Radius Does Not Exceed 2

Discussiones Mathematicae Graph Theory, 2020
Let A(G) and D(G) be the adjacency matrix and the degree matrix of a graph G, respectively. For any real α ∈ [0, 1], we consider Aα (G) = αD(G) + (1 − α)A(G) as a graph matrix, whose largest eigenvalue is called the Aα -spectral radius of G.
Wang Jian Feng, Wang Jing, Liu Xiaogang, Belardo Francesco   +3 more
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Directed random geometric graphs: structural and spectral properties

Journal of Physics: Complexity, 2022
In this work we analyze structural and spectral properties of a model of directed random geometric graphs: given n vertices uniformly and independently distributed on the unit square, a directed edge is set between two vertices if their distance is ...
Kevin Peralta-Martinez, J A Méndez-Bermúdez   +1 more
doaj   +1 more source

Vertex adjacency matrix and edge adjacency matrix of a sample graph network.

, 2023
Vertex adjacency matrix and edge adjacency matrix of a sample graph network.
Ertugrul Taciroglu (17692267), Sven Malama (17692264), Debasish Jana (1953253), Sriram Narasimhan (4403962)   +3 more
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On the A_α-Spectral Radii of Cactus Graphs

Mathematics, 2020
Let A ( G ) be the adjacent matrix and D ( G ) the diagonal matrix of the degrees of a graph G, respectively. For 0 ≤ α ≤ 1 , the A α -matrix is the general adjacency and signless Laplacian spectral matrix having the form of
Chunxiang Wang, Shaohui Wang, Jia-Bao Liu, Bing Wei   +3 more
doaj   +1 more source

Graphs with Clusters Perturbed by Regular Graphs—Aα-Spectrum and Applications

Discussiones Mathematicae Graph Theory, 2020
Given a graph G, its adjacency matrix A(G) and its diagonal matrix of vertex degrees D(G), consider the matrix Aα (G) = αD(G) + (1 − α)A(G), where α ∈ [0, 1).
Cardoso Domingos M., Pastén Germain, Rojo Oscar   +2 more
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Schema of the adjacency matrix.

, 2023
The elements of the adjacency matrix are the weights of links. Each row of the adjacency matrix contains the weights of in-links for the corresponding node, and the number of nonzero entries is its in-degree. Similarly, each column carries the weights of
Ilias Rentzeperis (10215602), Jia Li (160557), Cees van Leeuwen (255734)   +2 more
core   +1 more source