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math.CO2024
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…
math.CO2024★ 1 cited
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…
math.CO2024★ 1 cited
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…