论文信息 - Distinguishing numbers of Cartesian products of multiple complete graphs

Distinguishing numbers of Cartesian products of multiple complete graphs

We examine the distinguishing number of the Cartesian product of an arbitrary number of complete graphs. We show that for u 1 ≤ ... ≤ u d the distinguishing number of the Cartesian product of complete graphs of these sizes is either ⌈ u d 1/ s ⌉ or ⌈ u d 1/ s ⌉ + 1 where s = Π i = 1 d − 1 u i . In most cases, which of these values it is can be explicitly determined.

Garth Isaak | Michael J. Fisher

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