Geodesic
On the hyperdeterminants of Steiner distance hypermatrices
Ya-Nan Zheng1
1College of Mathematics and Information Science, Henan Normal University
The electronic journal of combinatorics, Tome 32 (2025) no. 2
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Let $G$ be a graph on $n$ vertices. The Steiner distance of a collection of $k$ vertices in $G$ is the fewest number of edges in any connected subgraph containing those vertices. The order $k$ Steiner distance hypermatrix of $G$ is the $n$-dimensional array indexed by vertices, whose entries are the Steiner distances of their corresponding indices. In this paper, we confirm a conjecture on the Steiner distance hypermatrices proposed by Cooper and Du [Electron. J. Combin. 31(3):\#P3.4, 2024]. Furthermore, we also compute the hyperdeterminant of the order $k$ Steiner distance hypermatrix of $P_{3}$.
DOI : 10.37236/13741
Classification : 05C12, 05C31, 15A69
Mots-clés : characteristic polynomial

Ya-Nan Zheng  1

1 College of Mathematics and Information Science, Henan Normal University 
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     title = {On the hyperdeterminants of {Steiner} distance hypermatrices},
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     doi = {10.37236/13741},
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Ya-Nan Zheng. On the hyperdeterminants of Steiner distance hypermatrices. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13741

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