Results 41 to 50 of about 359 (57)

Further results on the nullity of signed graphs [PDF]

, 2013
The nullity of a graph is the multiplicity of the eigenvalues zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges.
Liu, Yu, You, Lhua
core   +4 more sources

Totally frustrated states in the chromatic theory of gain graphs [PDF]

, 2006
We generalize proper coloring of gain graphs to totally frustrated states, where each vertex takes a value in a set of `qualities' or `spins' that is permuted by the gain group.
Zaslavsky, Thomas
core   +4 more sources

Eigenpairs of adjacency matrices of balanced signed graphs

Special Matrices
In this article, we study eigenvalues λ\lambda and their associated eigenvectors xx of the adjacency matrices AA of balanced signed graphs. Balanced signed graphs were first introduced and studied by Harary to handle a problem in social psychology ...
Chen Mei-Qin
doaj   +1 more source

On the weights of simple paths in weighted complete graphs

, 2012
Consider a weighted graph G with n vertices, numbered by the set {1,...,n}. For any path p in G, we call w_G(p) the sum of the weights of the edges of the path and we define the multiset {\cal D}_{i,j} (G) = {w_G(p) | p simple path between i and j} We ...
Rubei, Elena
core   +2 more sources

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

The Gap Number of the T-Tetromino

, 2014
A famous result of D. Walkup states that the only rectangles that may be tiled by the T-tetromino are those in which both sides are a multiple of four. In this paper we examine the rest of the rectangles, asking how many T-tetrominos may be placed into ...
Hochberg, Robert
core   +1 more source

Orientable ℤN-Distance Magic Graphs

Discussiones Mathematicae Graph Theory, 2019
Let G = (V, E) be a graph of order n. A distance magic labeling of G is a bijection ℓ: V → {1, 2, . . ., n} for which there exists a positive integer k such that ∑x∈N(v)ℓ(x) = k for all v ∈ V, where N(v) is the open neighborhood of v.
Cichacz Sylwia, Freyberg Bryan, Froncek Dalibor   +2 more
doaj   +1 more source

Signed graphs cospectral with the path

, 2018
A signed graph $\Gamma$ is said to be determined by its spectrum if every signed graph with the same spectrum as $\Gamma$ is switching isomorphic with $\Gamma$.
Akbari, Saieed, Haemers, Willem H., Maimani, Hamid Reza, Majd, Leila Parsaei   +3 more
core   +1 more source

Spectral Properties of Oriented Hypergraphs

, 2014
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an
Reff, Nathan
core   +1 more source

Signed graphs with strong (anti-)reciprocal eigenvalue property

Special Matrices
A (signed) graph is said to exhibit the strong reciprocal (anti-reciprocal) eigenvalue property (SR) (resp., (-SR)) if for any eigenvalue λ\lambda , it has 1λ\frac{1}{\lambda } (resp.,−1λ-\frac{1}{\lambda }) as an eigenvalue as well, with the same ...
Belardo Francesco, Huntington Callum
doaj   +1 more source