Geodesic
Counterexample to a conjecture on the structure of bipartite partitionable graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 527-540

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A graph G is called a prism fixer if γ(G×K₂) = γ(G), where γ(G) denotes the domination number of G. A symmetric γ-set of G is a minimum dominating set D which admits a partition D = D₁∪ D₂ such that V(G)-N[D_i] = D_j, i,j = 1,2, i ≠ j. It is known that G is a prism fixer if and only if G has a symmetric γ-set.
Keywords: domination, prism fixer, symmetric dominating set, bipartite graph 
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Gibson, Richard; Mynhardt, Christina. Counterexample to a conjecture on the structure of bipartite partitionable graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 527-540. http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a8/