# Edgeless graphs are the only universal fixers

Czechoslovak Mathematical Journal (2014)

- Volume: 64, Issue: 3, page 833-843
- ISSN: 0011-4642

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topWash, Kirsti. "Edgeless graphs are the only universal fixers." Czechoslovak Mathematical Journal 64.3 (2014): 833-843. <http://eudml.org/doc/262156>.

@article{Wash2014,

abstract = {Given two disjoint copies of a graph $G$, denoted $G^1$ and $G^2$, and a permutation $\pi $ of $V(G)$, the graph $\pi G$ is constructed by joining $u \in V(G^1)$ to $\pi (u) \in V(G^2)$ for all $u \in V(G^1)$. $G$ is said to be a universal fixer if the domination number of $\pi G$ is equal to the domination number of $G$ for all $\pi $ of $V(G)$. In 1999 it was conjectured that the only universal fixers are the edgeless graphs. Since then, a few partial results have been shown. In this paper, we prove the conjecture completely.},

author = {Wash, Kirsti},

journal = {Czechoslovak Mathematical Journal},

keywords = {universal fixer; domination; universal fixer; domination number; prism},

language = {eng},

number = {3},

pages = {833-843},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Edgeless graphs are the only universal fixers},

url = {http://eudml.org/doc/262156},

volume = {64},

year = {2014},

}

TY - JOUR

AU - Wash, Kirsti

TI - Edgeless graphs are the only universal fixers

JO - Czechoslovak Mathematical Journal

PY - 2014

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 64

IS - 3

SP - 833

EP - 843

AB - Given two disjoint copies of a graph $G$, denoted $G^1$ and $G^2$, and a permutation $\pi $ of $V(G)$, the graph $\pi G$ is constructed by joining $u \in V(G^1)$ to $\pi (u) \in V(G^2)$ for all $u \in V(G^1)$. $G$ is said to be a universal fixer if the domination number of $\pi G$ is equal to the domination number of $G$ for all $\pi $ of $V(G)$. In 1999 it was conjectured that the only universal fixers are the edgeless graphs. Since then, a few partial results have been shown. In this paper, we prove the conjecture completely.

LA - eng

KW - universal fixer; domination; universal fixer; domination number; prism

UR - http://eudml.org/doc/262156

ER -

## References

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