Exploring Metric and Strong Metric Dimensions in Inclusion Ideal Graphs of Commutative Rings
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915332026793984 |
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| author | Dodongeh, E. Moussavi, A. Nikandish, R. |
| author_facet | Dodongeh, E. Moussavi, A. Nikandish, R. |
| contents | The inclusion ideal graph of a commutative unitary ring $R$ is the (undirected) graph $In(R)$ whose vertices all non-trivial ideals of $R$ and two distinct vertices are adjacent if and only if one of them is a proper subset of the other one. In this paper, the metric dimension of $In(R)$ is discussed. Moreover, the structure of the resolving graph of $In(R)$ is characterized and as an application, we compute the strong metric dimension of $In(R)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09696 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exploring Metric and Strong Metric Dimensions in Inclusion Ideal Graphs of Commutative Rings Dodongeh, E. Moussavi, A. Nikandish, R. Combinatorics The inclusion ideal graph of a commutative unitary ring $R$ is the (undirected) graph $In(R)$ whose vertices all non-trivial ideals of $R$ and two distinct vertices are adjacent if and only if one of them is a proper subset of the other one. In this paper, the metric dimension of $In(R)$ is discussed. Moreover, the structure of the resolving graph of $In(R)$ is characterized and as an application, we compute the strong metric dimension of $In(R)$. |
| title | Exploring Metric and Strong Metric Dimensions in Inclusion Ideal Graphs of Commutative Rings |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2308.09696 |