On the metric dimension of graphs associated with irreducible and Arf numerical semigroups
A subset Δ of non-negative integers [Formula: see text] is called a numerical semigroup if it is a submonoid of [Formula: see text] and has a finite complement in [Formula: see text]. A graph [Formula: see text] is called a [Formula: see text]-graph if there exists a numerical semigroup Δ with multi...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2024-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2350582 |
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| Summary: | A subset Δ of non-negative integers [Formula: see text] is called a numerical semigroup if it is a submonoid of [Formula: see text] and has a finite complement in [Formula: see text]. A graph [Formula: see text] is called a [Formula: see text]-graph if there exists a numerical semigroup Δ with multiplicity α and embedding dimension β such that [Formula: see text] and [Formula: see text]. In this article, we compute the [Formula: see text]-graphs for irreducible and Arf numerical semigroups having a metric dimension of 2. It is proved that if Δ be an irreducible and arf numerical semigroup then there are exactly 2 and 8 non-isomorphic [Formula: see text]-graphs respectively, whose metric dimension is 2. |
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| ISSN: | 0972-8600 2543-3474 |