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arXiv · 1911.08045

The k-Power Domination Number in Some Self-Similar Graphs

Yulun Xu·Qi Bao·Zhongzhi Zhang
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Abstract

The $k$-power domination problem is a problem in graph theory, which has applications in many areas. However, it is hard to calculate the exact $k$-power domination number since determining k-power domination number of a generic graph is a NP-complete problem. We determine the exact $k$-power domination number in two graphs which have the same number of vertices and edges: pseudofractal scale-free web and Sierpi\'nski gasket. The $k$-power domination number becomes 1 for $k\ge2$ in the Sierpi\'nski gasket, while the $k$-power domination number increases at an exponential rate with regard to the number of vertices in the pseudofractal scale-free web. The scale-free property may account for the difference in the behavior of two graphs.

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Yulun Xu, Qi Bao, Zhongzhi Zhang. 2019-11-19. The k-Power Domination Number in Some Self-Similar Graphs. https://arxiv.org/abs/1911.08045

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