Parametric Power Supply Networks

Consider a graph G in which each vertex is either a supply vertex or a demand vertex and is assigned a supply or a demand. Such a graph G is called a power supply network. All the supplies and demands are nonnegative constant numbers in an ordinary network, called a steady network [1].This thesis introduces a parametric power supply network, in which all the supplies and demands are functions of a parameter λ. The supply of a vertex v is denoted by sv(λ) and the demand by dv(λ). Figure 1 depicts steady networks; each supply vertex is drawn by a square, each demand vertex by a circle, and the supply or demand is written inside. Figure 2(a) depicts a parametric network, whose variable demands dv3(λ) and dv4(λ) are drawn in Fig. 2(b). Each