Abstract
In general, determining the domination number and the feedback vertex number 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 for a claw-free G with and thus determining the domination number of the complement of a claw-free G with is polynomial, where is the independence number of G. Furthermore, if a graph G is not a star, has no isolated vertex and isolated edge, then 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, provided For the case when is also given. Thereby, we are able to show that determining is polynomial.
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