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I'm interested in the explicit examples of graphs for which application of Goemans and Williamson algorithm for approximating maximum cuts results in 0.878…-approximation factor.

The algorithm to create such instances would be perfect, explicit examples and references are satisfactory.

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I guess this reference is about what you ask:

N. Alon, B. Sudakov, and U. Zwick. Constructing worst case instances for semidefinite programming based approximation algorithms. SIAM Journalon Discrete Mathematics, 15:58–72, 2002.

This is an excerpt from it (p.60):

... we present the construction of the graphs that show that the local analysis of the MAX CUT algorithms of [GW95] and [Zwi99] are tight.

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