  In this paper, we give a modified version of the qutrit ZX-calculus, by which
we represent qutrit graph states as diagrams and prove that the qutrit version
of local complementation property is true if and only if the qutrit Hadamard
gate $H$ has an Euler decomposition into $4\pi/3$-green and red rotations. This
paves the way for studying the completeness of qutrit ZX-calculus for qutrit
stabilizer quantum mechanics.
