Series–parallel graph

 In progress Series-parallel graphs is a mathematical model of series and parallel electric circuits with two distinguished nodes called terminals, one of them called source, another one called sink, indicating the direction of the electrical current flow.

Definition and terminology

There are several ways to define series-parallel graphs. The following defiition basically follows the one used in

A two-terminal graph (TTG) is a graph with two distinguished vertices, s and t called source and sink, respectively.

The parallel composition P = P(X,Y) of two TTGs X and Y is a TTG created from the disjoint union of graphs X and Y by merging the sources of X and Y to create the source of P and merging the sinks of X and Y to create the sink of P.

The series composition S = S(X,Y) of two TTGs X and Y is a TTG created from the disjoint union of graphs X and Y by merging the sink of X with the source of Y. The source of X becomes source of P and the sink of Y becomes the sink of P.