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- W4308585169 abstract "In general, determining the domination number γ(G) and the feedback vertex number τ(G) of a claw-free graph (even a line graph) is NP-hard. In contrast, the situation becomes different for the complement of a line graph. In this paper, it is shown that γ(G¯)≤3 for a claw-free G with α(G)≥3, and thus determining the domination number of the complement of a claw-free G with α(G)≥3 is polynomial, where α(G) is the independence number of G. Furthermore, if a graph G is not a star, has no isolated vertex and isolated edge, then 2≤γ(J(G))≤3, where J(G) is the complement of the line graph L(G) of G. If a graph G is not a star, and has no isolated vertex, τ(J(G))=n−Δ(G)−1, provided Δ(G)≥6. For the case when Δ(G)≤5, τ(J(G)) is also given. Thereby, we are able to show that determining τ(J(G)) is polynomial." @default.
- W4308585169 created "2022-11-12" @default.
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- W4308585169 date "2022-09-02" @default.
- W4308585169 modified "2023-09-25" @default.
- W4308585169 title "Domination number and feedback vertex number of complements of line graphs" @default.
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- W4308585169 doi "https://doi.org/10.1080/09728600.2022.2142863" @default.
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