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A paired dominating set of a graph G without isolated vertices is a dominating set of G whose induced subgraph has a perfect matching. The paired domination number γ pr (G) of G is the minimum cardinality amongst all paired dominating sets of G. The graph G is paired domination edge-critical (γ pr EC) if for every e ∈ E(G), γ pr (G + e) < γ pr (G). We… (More)

A graph G is called a prism fixer if γ(G × K 2) = 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 = D 1 ∪ D 2 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. Hartnell and Rall [On dominating… (More)

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