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- W2044262022 abstract "For a graph G with n vertices and a permutation α on V(G), a permutation graph P α (G) is obtained from two identical copies of G by adding an edge between v and α(V) for any v ϵ V(G). Let γ(G) be the domination number of a graph G. It has been shown that γ(G) ≤ γ(P α (G) ≤ 2γ(G) for any permutation α on V(G). In this paper, we investigate specific graphs for which there exists a permutation α such that γ(P α (G)) ≻ γ(G) in terms of the domination number of G or the maximum degree of G. Additionally, we construct a class of graphs for which the domination number of any permutation graph is twice the domination number of the original graph, as well as explore finding a specific graph G and permutation α for any two positive integers a and b with a ≤ b ≤ 2a, to have γ(G) = a and γ(P α (G)) = b." @default.
- W2044262022 created "2016-06-24" @default.
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- W2044262022 date "2009-09-01" @default.
- W2044262022 modified "2023-09-23" @default.
- W2044262022 title "BOUNDS ON THE DOMINATION NUMBER OF PERMUTATION GRAPHS" @default.
- W2044262022 cites W1968949736 @default.
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- W2044262022 doi "https://doi.org/10.1142/s0219265909002522" @default.
- W2044262022 hasPublicationYear "2009" @default.
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