How to determine the structural number of a block graph by the cut-set method

A method for determining the structural number of a block graph, using the cut-set method, is outlined. An underlying concept is the structure support graph. The structure support, structural numbers describing the blocks, and cut-sets of the block graph are required to find the structural number of the whole block graph. Numerous graph-theoretical applications of the cut-set method in circuit theory are mentioned. Each connected block graph is shown to possess a structure support such that the corresponding linear graph is also a connected graph.