- Tytuł:
- Convex universal fixers
- Autorzy:
-
Lemańska, Magdalena
Zuazua, Rita - Powiązania:
- https://bibliotekanauki.pl/articles/743272.pdf
- Data publikacji:
- 2012
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
convex sets
dominating sets
universal fixers - Opis:
- In [1] Burger and Mynhardt introduced the idea of universal fixers. Let G = (V, E) be a graph with n vertices and G' a copy of G. For a bijective function π: V(G) → V(G'), define the prism πG of G as follows: V(πG) = V(G) ∪ V(G') and $E(πG) = E(G) ∪ E(G') ∪ M_{π}$, where $M_{π} = {u π(u) | u ∈ V(G)}$. Let γ(G) be the domination number of G. If γ(πG) = γ(G) for any bijective function π, then G is called a universal fixer. In [9] it is conjectured that the only universal fixers are the edgeless graphs K̅ₙ. In this work we generalize the concept of universal fixers to the convex universal fixers. In the second section we give a characterization for convex universal fixers (Theorem 6) and finally, we give an in infinite family of convex universal fixers for an arbitrary natural number n ≥ 10.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2012, 32, 4; 807-812
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł