The domination polynomial of powers of paths and cycles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911999955304448 |
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| author | Galvin, David Zhang, Yufei |
| author_facet | Galvin, David Zhang, Yufei |
| contents | A dominating set in a graph is a set of vertices with the property that every vertex in the graph is either in the set or adjacent to something in the set. The domination sequence of the graph is the sequence whose $k$th term is the number of dominating sets of size $k$.
Alikhani and Peng have conjectured that the domination sequence of every graph is unimodal. Beaton and Brown verified this conjecture for paths and cycles. Here we extend this to arbitrary powers of paths and cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12731 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The domination polynomial of powers of paths and cycles Galvin, David Zhang, Yufei Combinatorics 05C31 A dominating set in a graph is a set of vertices with the property that every vertex in the graph is either in the set or adjacent to something in the set. The domination sequence of the graph is the sequence whose $k$th term is the number of dominating sets of size $k$. Alikhani and Peng have conjectured that the domination sequence of every graph is unimodal. Beaton and Brown verified this conjecture for paths and cycles. Here we extend this to arbitrary powers of paths and cycles. |
| title | The domination polynomial of powers of paths and cycles |
| topic | Combinatorics 05C31 |
| url | https://arxiv.org/abs/2408.12731 |