Generalized power domination in claw-free regular graphs

Hangdi Chen; Changhong Lu; Qingjie Ye

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arXiv · 1905.11655

Generalized power domination in claw-free regular graphs

Hangdi Chen·Changhong Lu·Qingjie Ye

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Abstract

In this paper, we give a series of couterexamples to negate a conjecture and hence answer an open question on the $k$-power domination of regular graphs (see [P. Dorbec et al., SIAM J. Discrete Math., 27 (2013), pp. 1559-1574]). Furthermore, we focus on the study of $k$-power domination of claw-free graphs. We show that for $l\in\{2,3\}$ and $k\ge l$, the $k$-power domination number of a connected claw-free $(k+l+1)$-regular graph on $n$ vertices is at most $\frac{n}{k+l+2}$, and this bound is tight.

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Hangdi Chen, Changhong Lu, Qingjie Ye. 2020-10-23. Generalized power domination in claw-free regular graphs. https://arxiv.org/abs/1905.11655

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