A Characterization of Oriented Hypergraphic Laplacian and Adjacency Matrix Coefficients

Abstract

An oriented hypergraph is an oriented incidence structure that generalizes and unifies graph and hypergraph theoretic results by examining its locally signed graphic substructure. In this paper we obtain a combinatorial characterization of the coefficients of the characteristic polynomials of oriented hypergraphic Laplacian and adjacency matrices via a signed hypergraphic generalization of basic figures of graphs. Additionally, we provide bounds on the determinant and permanent of the Laplacian matrix, characterize the oriented hypergraphs in which the upper bound is sharp, and demonstrate that the lower bound is never achieved.

References in corpus (3)

• Spectral Properties of Complex Unit Gain Graphs
• An Oriented Hypergraphic Approach to Algebraic Graph Theory
• On Blow-Ups and Injectivity of Quivers

Cited by in corpus (12)

• Spectral Theory of Laplace Operators on Oriented Hypergraphs
• Incidence Hypergraphs: Injectivity, Uniformity, and Matrix-tree Theorems
• Normalized Laplace Operators for Hypergraphs with Real Coefficients
• Coloring the normalized Laplacian for oriented hypergraphs
• Sharp bounds for the largest eigenvalue
• Oriented Hypergraphic Matrix-tree Type Theorems and Bidirected Minors via Boolean Order Ideals
• Geometry and symmetry in biochemical reaction systems
• Spectra of hyperstars on public transportation networks
• Incidence Hypergraphs: Box Products & the Laplacian
• Spectral classes of hypergraphs
• Generalizing Kirchhoff laws for Signed Graphs
• The Determinant of $\{\pm 1\}$-Matrices and Oriented Hypergraphs