Question in paper for accelerated sampling formula

[LokiXun]

Hi, It's a work with great impact. And I had a problem to understand the formula in eq52 (Accelerate sampling). May I wondering that:

1. why eq52 have a additional item $$\prod{q_{\sigma,\tau}}(x_t \mid x_0)$$ when compared to eq6
2. what is the forms a star graph. means?

Thanks. @jiamings