Graphs with isolation number equal to one third of the order
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917660453765120 |
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| author | Lemanska, Magdalena Mora, Mercè Souto-Salorio, María José |
| author_facet | Lemanska, Magdalena Mora, Mercè Souto-Salorio, María José |
| contents | A set $D$ of vertices of a graph $G$ is isolating if the set of vertices not in $D$ or with no neighbor in $D$ is independent. The isolation number of $G$, denoted by $ι(G)$, is the minimum cardinality of an isolating set of $G$. It is known that $ι(G)\le n/3$, if $G$ is a connected graph of order $n$, $n\ge 3$, distinct from $C_5$. The main result of this work is the characterisation of unicyclic and block graphs of order $n$ with isolating number equal to $n/3$. Moreover, we provide a family of general graphs attaining this upper bound on the isolation number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11520 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Graphs with isolation number equal to one third of the order Lemanska, Magdalena Mora, Mercè Souto-Salorio, María José Combinatorics 05C69 A set $D$ of vertices of a graph $G$ is isolating if the set of vertices not in $D$ or with no neighbor in $D$ is independent. The isolation number of $G$, denoted by $ι(G)$, is the minimum cardinality of an isolating set of $G$. It is known that $ι(G)\le n/3$, if $G$ is a connected graph of order $n$, $n\ge 3$, distinct from $C_5$. The main result of this work is the characterisation of unicyclic and block graphs of order $n$ with isolating number equal to $n/3$. Moreover, we provide a family of general graphs attaining this upper bound on the isolation number. |
| title | Graphs with isolation number equal to one third of the order |
| topic | Combinatorics 05C69 |
| url | https://arxiv.org/abs/2307.11520 |