Discrete isoperimetric inequalities on the strong products of paths
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915533149962240 |
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| author | Wang, Runze |
| author_facet | Wang, Runze |
| contents | For a graph $G=(V,\ E)$ and a nonempty set $S\subseteq V$, the \emph{vertex boundary} of $S$, denoted by $\partial_G(S)$, is defined to be the set of vertices that are not in $S$ but have at least one neighbor in $S$. In this paper, for $G$ being a strong product of two paths, we determine the cases in which $|\partial_G(S)|$ is minimized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete isoperimetric inequalities on the strong products of paths Wang, Runze Combinatorics 05C35 For a graph $G=(V,\ E)$ and a nonempty set $S\subseteq V$, the \emph{vertex boundary} of $S$, denoted by $\partial_G(S)$, is defined to be the set of vertices that are not in $S$ but have at least one neighbor in $S$. In this paper, for $G$ being a strong product of two paths, we determine the cases in which $|\partial_G(S)|$ is minimized. |
| title | Discrete isoperimetric inequalities on the strong products of paths |
| topic | Combinatorics 05C35 |
| url | https://arxiv.org/abs/2502.12199 |