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 in | The Electronic journal of combinatorics Vol. 32; no. 2 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
23.05.2025
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| Online Access | Get full text |
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| Summary: | 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 $P_{3}$. |
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| ISSN: | 1077-8926 1077-8926 |
| DOI: | 10.37236/13741 |