Vertex reducibility for the grand potential

To solve this problem we denote by nj the number of irreducible parts and by ur the number of reducible vertices, and we note that 

The sum of all diagrams with a marked vertex yields - u( (p(r))y = — uqc2, where the factor 1/2 takes into account the symmetry of the vertex. Equation (5.31) results  

Grand Canonical Description of Solutions at Finite Concentration 

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