Existence of independent [1, 2]-sets in caterpillars
Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacent and for every vertex ν ∈ V (G)\S, 1 ≤ |N(ν) ∩ S| ≤ 2, that is, every vertex ν ∈ V (G)\S is adjacent to at least one but not more than two vertices in S. In this paper, we discuss the existence of in...
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| Main Authors: | , |
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| Format: | text |
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Archīum Ateneo
2016
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| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/45 https://aip.scitation.org/doi/abs/10.1063/1.4940820 |
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| Institution: | Ateneo De Manila University |
| Summary: | Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacent and for every vertex ν ∈ V (G)\S, 1 ≤ |N(ν) ∩ S| ≤ 2, that is, every vertex ν ∈ V (G)\S is adjacent to at least one but not more than two vertices in S. In this paper, we discuss the existence of independent [1, 2]-sets in a family of trees called caterpillars. |
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