Results 11 to 20 of about 150,247 (249)

The anti-adjacency matrix of a graph: Eccentricity matrix

Discrete Applied Mathematics, 2018
In this paper we introduce a new graph matrix, named the anti-adjacency matrix or eccentricity matrix, which is constructed from the distance matrix of a graph by keeping for each row and each column only the largest distances.
Jianfeng Wang, Mei Lu, Francesco Belardo, M. Randic   +3 more
semanticscholar   +3 more sources

On the adjacency matrix of a block graph

Linear and Multilinear Algebra, 2014
R. Bapat, Souvik Roy
semanticscholar   +3 more sources

Wiener index and addressing of some finite graphs

AKCE International Journal of Graphs and Combinatorics, 2023
An addressing of length t of a graph G is an assignment of t-tuples with entries in [Formula: see text] called addresses, to the vertices of G such that the distance between any two vertices can be determined from their addresses.
Mona Gholamnia Taleshani, Ahmad Abbasi
doaj   +1 more source

A Note on Some Bounds of the α-Estrada Index of Graphs

Advances in Mathematical Physics, 2020
Let G be a simple graph with n vertices. Let A~αG=αDG+1−αAG, where 0≤α≤1 and AG and DG denote the adjacency matrix and degree matrix of G, respectively. EEαG=∑i=1neλi is called the α-Estrada index of G, where λ1,⋯,λn denote the eigenvalues of A~αG.
Yang Yang, Lizhu Sun, Changjiang Bu
doaj   +1 more source

New Bounds for the α-Indices of Graphs

Mathematics, 2020
Let G be a graph, for any real 0≤α≤1, Nikiforov defines the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and diagonal matrix of degrees of the vertices of G.
Eber Lenes, Exequiel Mallea-Zepeda, Jonnathan Rodríguez   +2 more
doaj   +1 more source

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

On bounding the bandwidth of graphs with symmetry [PDF]

, 2015
We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semidefinite programming relaxation of the minimum cut problem is obtained by strengthening the known semidefinite ...
Sotirov, Renata, van Dam, Edwin R.
core   +3 more sources

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
doaj   +1 more source

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

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