Geodesic
Distinguishing numbers of Cartesian products of multiple complete graphs
Ars Mathematica Contemporanea, Tome 5 (2012) no. 1, pp. 159-173.

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We examine the distinguishing number of the Cartesian product of an arbitrary number of complete graphs. We show that for u1 ≤ ... ≤ ud the distinguishing number of the Cartesian product of complete graphs of these sizes is either ⌈ud1/s⌉ or ⌈ud1/s⌉ + 1 where s = Πi = 1d − 1 ui. In most cases, which of these values it is can be explicitly determined. 
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Michael J. Fisher; Garth Isaak. Distinguishing numbers of Cartesian products of multiple complete graphs. Ars Mathematica Contemporanea, Tome 5 (2012) no. 1, pp. 159-173. doi : 10.26493/1855-3974.245.348. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.245.348/

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