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A general switching method for constructing E-cospectral hypergraphs
Aida Abiad, Joshua Cooper, Utku Okur
Spectral hypergraph theory studies the structural properties of a hypergraph that can be inferred from the eigenvalues and the eigenvectors of either matrices or tensors associated…
Determinants of Steiner Distance Hypermatrices
Joshua Cooper, Zhibin Du
Generalizing work from the 1970s on the determinants of distance hypermatrices of trees, we consider the hyperdeterminants of order- Steiner distance hypermatrices of trees on $…
Distance Critical Graphs
Joshua Cooper, Gabrielle Tauscheck
In 1971, Graham and Pollak provided a formula for the determinant of the distance matrix of any tree on vertices. Yan and Yeh reproved this by exploiting the fact that pendant…
Note on the spectra of Steiner distance hypermatrices
Joshua Cooper, Zhibin Du
The Steiner distance of a set of vertices in a graph is the fewest number of edges in any connected subgraph containing those vertices. The order- Steiner distance hypermatrix o…
A Generalization of the Graham-Pollak Tree Theorem to Even-Order Steiner Distance
Joshua Cooper, Gabrielle Tauscheck
Graham and Pollak showed in 1971 that the determinant of a tree's distance matrix depends only on its number of vertices, and, in particular, it is always nonzero. The Steiner dist…