Locating minimal framing oriented tree graphs

The article considers a generalized problem of a minimal framing tree graph, that is, a problem with asymmetric matrix of weight coefficients of arcs where the solution is an oriented tree graph. The article includes mathematical models of quadratic programming, including a model with a minimum number of linear constraints the generalized minimal framing tree graph problem is reduced to. We consider finding the minimal framing tree graph when the number of the root, transit, or hanging vertex is given, as well as the case of several conditions. Examples are provided; mathematical models are solved with the help of the Excel.