  Recently M.E. Shirokov introduced the non-commutative operator graph
depending on the complex parameter $\theta $ to construct channels with
positive quantum zero-error capacity having vanishing n-shot capacity. We study
the algebraic structure of this graph. The relations for the algebra generated
by the graph are derived. In the limiting case $\theta =\pm1$ the graph becomes
abelian and degenerates into the direct sum of four one-dimensional irreducible
representations of the Klein group.
