Niche Hypergraphs of Products of Digraphs
If D = (V, A) is a digraph, its niche hypergraph Nℋ(D) = (V, ℰ) has the edge set ℰ={e⊆V||e|≥2∧∃ υ∈V:e=ND−(υ)∨e=ND+(υ)}{\cal E} = \{ {e \subseteq V| | e | \ge 2 \wedge \exists \, \upsilon \in V:e = N_D^ - ( \upsilon ) \vee e = N_D^ + ( \upsilon )} \} . Niche hypergraphs generalize the well-known nic...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Zielona Góra
2020-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2138 |
| _version_ | 1827832793795657728 |
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| author | Sonntag Martin Teichert Hanns-Martin |
| author_facet | Sonntag Martin Teichert Hanns-Martin |
| author_sort | Sonntag Martin |
| collection | DOAJ |
| description | If D = (V, A) is a digraph, its niche hypergraph Nℋ(D) = (V, ℰ) has the edge set
ℰ={e⊆V||e|≥2∧∃ υ∈V:e=ND−(υ)∨e=ND+(υ)}{\cal E} = \{ {e \subseteq V| | e | \ge 2 \wedge \exists \, \upsilon \in V:e = N_D^ - ( \upsilon ) \vee e = N_D^ + ( \upsilon )} \}
. Niche hypergraphs generalize the well-known niche graphs and are closely related to competition hypergraphs as well as common enemy hypergraphs. For several products D1 ◦ D2 of digraphs D1 and D2, we investigate the relations between the niche hypergraphs of the factors D1, D2 and the niche hypergraph of their product D1 ◦ D2. |
| first_indexed | 2024-03-12T05:19:48Z |
| format | Article |
| id | doaj.art-7a12a4c89d0a4a729b0cdb3828d8bdff |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T05:19:48Z |
| publishDate | 2020-02-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-7a12a4c89d0a4a729b0cdb3828d8bdff2023-09-03T07:47:23ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922020-02-0140127929510.7151/dmgt.2138dmgt.2138Niche Hypergraphs of Products of DigraphsSonntag Martin0Teichert Hanns-Martin1Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, Prüferstraße 1, D–09596Freiberg, GermanyInstitute of Mathematics, University of Lübeck, Ratzeburger Allee 160, D–23562Lübeck, GermanyIf D = (V, A) is a digraph, its niche hypergraph Nℋ(D) = (V, ℰ) has the edge set ℰ={e⊆V||e|≥2∧∃ υ∈V:e=ND−(υ)∨e=ND+(υ)}{\cal E} = \{ {e \subseteq V| | e | \ge 2 \wedge \exists \, \upsilon \in V:e = N_D^ - ( \upsilon ) \vee e = N_D^ + ( \upsilon )} \} . Niche hypergraphs generalize the well-known niche graphs and are closely related to competition hypergraphs as well as common enemy hypergraphs. For several products D1 ◦ D2 of digraphs D1 and D2, we investigate the relations between the niche hypergraphs of the factors D1, D2 and the niche hypergraph of their product D1 ◦ D2.https://doi.org/10.7151/dmgt.2138niche hypergraphproduct of digraphscompetition hypergraph05c6505c7605c20 |
| spellingShingle | Sonntag Martin Teichert Hanns-Martin Niche Hypergraphs of Products of Digraphs Discussiones Mathematicae Graph Theory niche hypergraph product of digraphs competition hypergraph 05c65 05c76 05c20 |
| title | Niche Hypergraphs of Products of Digraphs |
| title_full | Niche Hypergraphs of Products of Digraphs |
| title_fullStr | Niche Hypergraphs of Products of Digraphs |
| title_full_unstemmed | Niche Hypergraphs of Products of Digraphs |
| title_short | Niche Hypergraphs of Products of Digraphs |
| title_sort | niche hypergraphs of products of digraphs |
| topic | niche hypergraph product of digraphs competition hypergraph 05c65 05c76 05c20 |
| url | https://doi.org/10.7151/dmgt.2138 |
| work_keys_str_mv | AT sonntagmartin nichehypergraphsofproductsofdigraphs AT teicherthannsmartin nichehypergraphsofproductsofdigraphs |