科研之友
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摘要
In this paper, we give a series of counterexamples to negate a conjecture and answer an open question on the k-power domination of regular graphs [see Dorbec et al. (SIAM J Discrete Math 27:1559-1574, 2013)]. Furthermore, we focus on the study of k-power domination of claw-free graphs. We show that for l is an element of {2, 3} and k >= l, the k-power domination number of a connected claw-free (k + l +1)-regular graph on n vertices is at most n/k+l+2 and this bound is tight.
