ON THE COMBINATORICS OF BINARY SERIES-PARALLEL GRAPHS

Binary series-parallel (bsp) graphs have applications in transportation modeling, and exhibit interesting combinatorial properties. This work is limited to the second aspect. The bsp graphs of a given size -measured in edges - are enumerated. Under a uniform probability model, we investigate the asymptotic distribution of the order (number of vertices) and the asymptotic average length of a random walk (under different strategies) of large graphs of the same size. The systematic method throughout is to define the graphs, and the features we evaluate by a structural equation (equivalent to a regular expression). The structural equation is translated into an equation for a generating function, which is then analyzed.