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arXiv · 1601.01268

The number of dominating $k$-sets of paths, cycles and wheels

Jorge L. Arocha·Bernardo Llano
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Abstract

We give a shorter proof of the recurrence relation for the domination polynomial $γ(P_{n},t)$ and for the number $γ_{k}(P_{n})$ of dominating $k$-sets of the path with $n$ vertices. For every positive integers $n$ and $k,$ numbers $γ_{k}(P_{n})$ are determined solving a problem posed by S. Alikhani in CID 2015. Moreover, the numbers of dominating $k$-sets $γ_{k}(C_{n})$ of cycles and $γ_{k}(W_{n})$ of wheels with $n$ vertices are computed.

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BibTeXRIS

Jorge L. Arocha, Bernardo Llano. 2016-01-06. The number of dominating $k$-sets of paths, cycles and wheels. https://arxiv.org/abs/1601.01268

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