Enumeration of labeled bi-block graphs

A bi-block graph is a connected graph in which all blocks are complete bipartite graphs. Labeled bi-block graphs and bridgeless bi-block graphs are enumerated exactly and asymptotically by the number of vertices. It is proved that almost all labeled connected bi-block graphs have no bridges. In addition, planar bi-block graphs are enumerated, and an asymptotic estimate is found for the number of such graphs. Tab. 1, bibliogr. 12.