Distance 2-Domination in Prisms of Graphs
A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G) − D) and D is at most two. Let γ2(G) denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2017-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1946 |
| _version_ | 1797717997541916672 |
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| author | Hurtado Ferran Mora Mercè Rivera-Campo Eduardo Zuazua Rita |
| author_facet | Hurtado Ferran Mora Mercè Rivera-Campo Eduardo Zuazua Rita |
| author_sort | Hurtado Ferran |
| collection | DOAJ |
| description | A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G) − D) and D is at most two. Let γ2(G) denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the graph πG obtained from G and a copy G′ of G by joining u ∊ V(G) with v′ ∊ V(G′) if and only if v′ = π(u). If γ2(πG) = γ2(G) for any permutation π of V(G), then G is called a universal γ2-fixer. In this work we characterize the cycles and paths that are universal γ2-fixers. |
| first_indexed | 2024-03-12T08:44:35Z |
| format | Article |
| id | doaj.art-1e6b60d5f1514b2b86dce92d5990dd3d |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T08:44:35Z |
| publishDate | 2017-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-1e6b60d5f1514b2b86dce92d5990dd3d2023-09-02T16:29:33ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922017-05-0137238339710.7151/dmgt.1946dmgt.1946Distance 2-Domination in Prisms of GraphsHurtado Ferran0Mora Mercè1Rivera-Campo Eduardo2Zuazua Rita3Universitat Politècnica de Catalunya Barcelona, SpainUniversitat Politècnica de Catalunya Barcelona, SpainUniversidad Autónoma Metropolitana-Iztapalapa, MexicoUniversidad Nacional Autónoma de México, MexicoA set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G) − D) and D is at most two. Let γ2(G) denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the graph πG obtained from G and a copy G′ of G by joining u ∊ V(G) with v′ ∊ V(G′) if and only if v′ = π(u). If γ2(πG) = γ2(G) for any permutation π of V(G), then G is called a universal γ2-fixer. In this work we characterize the cycles and paths that are universal γ2-fixers.https://doi.org/10.7151/dmgt.1946distance 2 dominating setprisms of graphsuniversal fixer |
| spellingShingle | Hurtado Ferran Mora Mercè Rivera-Campo Eduardo Zuazua Rita Distance 2-Domination in Prisms of Graphs Discussiones Mathematicae Graph Theory distance 2 dominating set prisms of graphs universal fixer |
| title | Distance 2-Domination in Prisms of Graphs |
| title_full | Distance 2-Domination in Prisms of Graphs |
| title_fullStr | Distance 2-Domination in Prisms of Graphs |
| title_full_unstemmed | Distance 2-Domination in Prisms of Graphs |
| title_short | Distance 2-Domination in Prisms of Graphs |
| title_sort | distance 2 domination in prisms of graphs |
| topic | distance 2 dominating set prisms of graphs universal fixer |
| url | https://doi.org/10.7151/dmgt.1946 |
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