On calculations of many-loop diagrams of perturbation theory

A number of identities is formulated for semi-unique vertices and semi-unique triangles which are present in the diagrams of perturbation theory with massless scalar particles. Using these identities the reduction scheme can be developed which makes it possible to calculate many-loop diagrams without expanding into infinite series over the Hegenbauer polynomials and without performing any differentiations which bring additional kinematical complications. As a result, the calculation of many-loop diagrams of perturbation theory is significantly simplified