26 citations · 74 across the 46 of their papers we have counts for
56 papers
Hitting all maximal independent sets in -hollow graphs
Joshua Cooper, Isaiah Hollars
Fix a constant with . We say a graph on vertices is -hollow if every maximal independent set of has size at least . Denote by the size of a sma…
A Generalization of the Graham-Pollak Tree Theorem to Steiner Distance
Joshua Cooper, Gabrielle Tauscheck
Graham and Pollak showed that the determinant of the distance matrix of a tree depends only on the number of vertices of . Graphical distance, a function of pairs of vertice…
Zero loci of nullvectors and skew zero forcing in graphs and hypergraphs
Joshua Cooper, Grant Fickes
There is interesting internal structure in the nullspaces of graph and hypergraph adjacency matrices, especially for trees, bipartite graphs, and related combinatorial classes. The…
Positive-Definite Matrices over Finite Fields
Joshua Cooper, Erin Hanna, Hays Whitlatch
The study of positive-definite matrices has focused on Hermitian matrices, that is, square matrices with complex (or real) entries that are equal to their own conjugate transposes.…
Applications of the Harary-Sachs Theorem for Hypergraphs
Gregory J. Clark, Joshua Cooper
The Harary-Sachs theorem for -uniform hypergraphs equates the codegree- coefficient of the adjacency characteristic polynomial of a uniform hypergraph with a weighted sum of…
Geometric vs Algebraic Nullity for Hyperpaths
Joshua Cooper, Grant Fickes
We consider the question of how the eigenvarieties of a hypergraph relate to the algebraic multiplicities of their corresponding eigenvalues. Specifically, we (1) fully describe th…