On the Hyperdeterminants of Steiner Distance Hypermatrices

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...

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Published inThe Electronic journal of combinatorics Vol. 32; no. 2
Main Author Zheng, Ya-Nan
Format Journal Article
LanguageEnglish
Published 23.05.2025
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Abstract 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 $P_{3}$.
AbstractList 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 $P_{3}$.
Author Zheng, Ya-Nan
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Snippet 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...
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