Combinational analysis of the overlapping problem for vertices with more than four legs. II. Higher Legendre transforms

The properties of the graphs of the $m$-th Legendre transformation $\Gamma^{(m)}(\varepsilon_1,\dots,\varepsilon_m;A_{m+1},\dots,A_n)$ of the connected Green function generating functional ($\varepsilon_1,\dots,\varepsilon_m$ being dressed variables [7], $A_{m+1},\dots,A_n$ being bare ones) are considered. This gives an opportunity to find the explicite expression for the sum of all sceleton graphs included in the representation of; the dressed $k$-leg vertex, $k\leqslant m$, and containing nontrivial $l$-leg subgraphs, $l\leqslant k$.