Geodesic
Convex universal fixers
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 4, pp. 807-812

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: convex sets, dominating sets, universal fixers 
@article{DMGT_2012_32_4_a14,
     author = {Lema\'nska, Magdalena and Zuazua, Rita},
     title = {Convex universal fixers},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {807--812},
     publisher = {mathdoc},
     volume = {32},
     number = {4},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2012_32_4_a14/}
}
TY  - JOUR
AU  - Lemańska, Magdalena
AU  - Zuazua, Rita
TI  - Convex universal fixers
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2012
SP  - 807
EP  - 812
VL  - 32
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2012_32_4_a14/
LA  - en
ID  - DMGT_2012_32_4_a14
ER  - 
%0 Journal Article
%A Lemańska, Magdalena
%A Zuazua, Rita
%T Convex universal fixers
%J Discussiones Mathematicae. Graph Theory
%D 2012
%P 807-812
%V 32
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2012_32_4_a14/
%G en
%F DMGT_2012_32_4_a14
Lemańska, Magdalena; Zuazua, Rita. Convex universal fixers. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 4, pp. 807-812. http://geodesic.mathdoc.fr/item/DMGT_2012_32_4_a14/