Results 101 to 110 of about 292 (163)

Kernels of directed graph Laplacians [PDF]

, 2020
. Let G denote a directed graph with adjacency matrix Q and in-degree matrix D. We consider the Kirchhoff matrix L = D−Q, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity
J S Caughman, J J P Veerman
core  

A Laplacian eigenbasis for threshold graphs

Special Matrices
Let GG be a graph on nn vertices. In this article, we prove that an eigenbasis of the Laplacian matrix of a star graph of order nn is also an eigenbasis of GG if and only if GG is a threshold graph. As an application of this spectral characterization, we
Macharete Rafael R., Del-Vecchio Renata R., Teixeira Heber, de Lima Leonardo   +3 more
doaj   +1 more source

A New Decomposition of the Graph Laplacian and the Binomial Structure of Mass-Action Systems. [PDF]

J Nonlinear Sci, 2023
Müller S.
europepmc   +1 more source

Laplacian spectral radius and some Hamiltonian properties of graphs, manuscript

, 2014
. Using upper bounds for the spectral radius of graphs established by Cao, we in this note present sufficient conditions which are based on the spectral radius for some Hamiltonian properties of graphs. Keywords: Spectral radius, Hamiltonian property AMS
Rao Li
core  

Zero Forcing Sets and Bipartite Circulants

, 2010
In this paper we introduce a class of regular bipartite graphs whose biadja-cency matrices are circulant matrices and we describe some of their properties. Notably, we compute upper and lower bounds for the zero forcing number for such a graph based only
Seth A. Meyer
core  

Long cycles in 3-connected graphs in orientable surfaces

, 2002
In this paper we apply a cutting theorem of Thomassen to show that there is a function f: N → N such that if G is a 3-connected graph which can be embedded in the orientable surface of genus g with face-width at least f(g), then G contains a cycle of ...
Xingxing Yu
core  

Note on the product of the largest and the smallest eigenvalue of a graph

Special Matrices
In this note, we use eigenvalue interlacing to derive an inequality between a graph’s maximum degree and its maximum and minimum adjacency eigenvalues. The equality case is fully characterized.
Abiad Aida, Dalfó Cristina, Fiol Miquel Àngel   +2 more
doaj   +1 more source

On the minimum spectral radius of connected graphs of given order and size

Special Matrices
In this article, we study a question of Hong from 1993 related to the minimum spectral radii of the adjacency matrices of connected graphs of given order and size.
Cioaba Sebastian M., Gupta Vishal, Marques Celso   +2 more
doaj   +1 more source

The zero divisor graph of 2 x 2 matrices over a field

, 2016
A zero divisor graph, Γ(R), is formed from a ring R by having each element of Z(R)\{0} to be a vertex in the graph and having two vertices u and v adjacent if the corresponding elements from the ring are nonequal and have product equal to zero.
Ashrafi, Ali Reza, Tadayyonfar, Adel
core  

Eigenvalues of complex unit gain graphs and gain regularity

Special Matrices
A complex unit gain graph (or T{\mathbb{T}}-gain graph) Γ=(G,γ)\Gamma =\left(G,\gamma ) is a gain graph with gains in T{\mathbb{T}}, the multiplicative group of complex units.
Brunetti Maurizio
doaj   +1 more source