Geodesic
Domination in Kn\"odel Graphs
Discrete mathematics & theoretical computer science, Tome 24 (2022) no. 1.

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Given a graph and an integer $k$, it is an NP-complete problem to decide whether there is a dominating set of size at most $k$. In this paper we study this problem for the Kn\"odel Graph on $n$ vertices using elementary number theory techniques. In particular, we show an explicit upper bound for the domination number of the Kn\"odel Graph on $n$ vertices any time that we can find a prime number $p$ dividing $n$ for which $2$ is a primitive root.
DOI : 10.46298/dmtcs.7158
Classification : 05C69 
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     author = {Racicot, Jesse and Rosso, Giovanni},
     title = {Domination in {Kn\"odel} {Graphs}},
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Racicot, Jesse; Rosso, Giovanni. Domination in Kn\"odel Graphs. Discrete mathematics & theoretical computer science, Tome 24 (2022) no. 1. doi : 10.46298/dmtcs.7158. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.7158/

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