40 research outputs found
Spectral Properties of Oriented Hypergraphs
An oriented hypergraph is a hypergraph where each vertex-edge incidence is
given a label of or . The adjacency and Laplacian eigenvalues of an
oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and
Laplacian matrices of an oriented hypergraph which depend on structural
parameters of the oriented hypergraph are found. An oriented hypergraph and its
incidence dual are shown to have the same nonzero Laplacian eigenvalues. A
family of oriented hypergraphs with uniformally labeled incidences is also
studied. This family provides a hypergraphic generalization of the signless
Laplacian of a graph and also suggests a natural way to define the adjacency
and Laplacian matrices of a hypergraph. Some results presented generalize both
graph and signed graph results to a hypergraphic setting.Comment: For the published version of the article see
http://repository.uwyo.edu/ela/vol27/iss1/24
Connected Hypergraphs with Small Spectral Radius
In 1970 Smith classified all connected graphs with the spectral radius at
most . Here the spectral radius of a graph is the largest eigenvalue of its
adjacency matrix. Recently, the definition of spectral radius has been extended
to -uniform hypergraphs. In this paper, we generalize the Smith's theorem to
-uniform hypergraphs. We show that the smallest limit point of the spectral
radii of connected -uniform hypergraphs is . We
discovered a novel method for computing the spectral radius of hypergraphs, and
classified all connected -uniform hypergraphs with spectral radius at most
.Comment: 20 pages, fixed a missing class in theorem 2 and other small typo