17 citations · 17 across the 5 of their papers we have counts for
5 papers
Oriented hypergraphs and generalizing the Harary-Sachs theorem to integer matrices
Blake Dvarishkis, Josephine Reynes, Lucas J. Rusnak
Incidence-based generalizations of cycle covers, called contributors, extend the Harary-Sachs coefficient theorem for characteristic polynomials of the adjacency matrix of graphs.…
Homogeneous Sets in Graphs and a Chromatic Multisymmetric Function
Logan Crew, Evan Haithcock, Josephine Reynes +1
In this paper, we extend the chromatic symmetric function to a chromatic -multisymmetric function , defined for graphs equipped with a partition of their vertex set int…
The Determinant of -Matrices and Oriented Hypergraphs
Lucas J. Rusnak, Josephine Reynes, Russell Li +2
The determinants of -matrices are calculated by via the oriented hypergraphic Laplacian and summing over an incidence generalization of vertex cycle-covers. These cycle-…
Generalizing Kirchhoff laws for Signed Graphs
Lucas J. Rusnak, Josephine Reynes, Skyler J. Johnson +1
Kirchhoff-type Laws for signed graphs are characterized by generalizing transpedances through the incidence-oriented structure of bidirected graphs. The classical -arborescence…
Incidence Hypergraphs: Injectivity, Uniformity, and Matrix-tree Theorems
Will Grilliette, Josephine Reynes, Lucas J. Rusnak
An oriented hypergraph is an oriented incidence structure that allows for the generalization of graph theoretic concepts to integer matrices through its locally signed graphic subs…