Stability of $2$-domination number of a graph
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916861733502976 |
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| author | Mehraban, Mazharuddin Alikhani, Saeid |
| author_facet | Mehraban, Mazharuddin Alikhani, Saeid |
| contents | This paper delves into the stability of the $2$-domination number in simple undirected graphs. The $2$-domination number of a graph $G$, $γ_2(G)$, represents the minimum size of a vertex subset where every other vertex in the graph is adjacent to at least two members of the subset. We define the $2$-domination stability, $st_{γ_2}(G)$, as the smallest number of vertices whose removal causes a change in $γ_2(G)$. Our primary contributions include computing this parameter for specific graphs, establishing various bounds for this stability and determining its behavior under certain graph operations combining two graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of $2$-domination number of a graph Mehraban, Mazharuddin Alikhani, Saeid Combinatorics 05C05, 05C69 This paper delves into the stability of the $2$-domination number in simple undirected graphs. The $2$-domination number of a graph $G$, $γ_2(G)$, represents the minimum size of a vertex subset where every other vertex in the graph is adjacent to at least two members of the subset. We define the $2$-domination stability, $st_{γ_2}(G)$, as the smallest number of vertices whose removal causes a change in $γ_2(G)$. Our primary contributions include computing this parameter for specific graphs, establishing various bounds for this stability and determining its behavior under certain graph operations combining two graphs. |
| title | Stability of $2$-domination number of a graph |
| topic | Combinatorics 05C05, 05C69 |
| url | https://arxiv.org/abs/2507.18535 |