On the extension of the class of split graphs

The extension of the class of split graphs, retaining a number of its advantages connected with algorithmic problems, is considered. One of its variations, the class of U-split graphs, is analyzed in detail. For this class solvability of the recognition problem and the problem of finding range of graph parameters in linear time concerning a number of vertices of a tested graph is proven. The generating function for the number of U-split graphs is given.