Maximal Resistor Networks

Edith Mooers

1. Introduction

In this paper I describe several resistor networks with n boundary
nodes and n(n-1)/2 resistors, such that all of the resistors in the
network can be determined from measurements of currents at the
boundary generated by imposed voltages.  I will call these
\emph{maximal} resistor networks.  First I describe a map of Dirichlet
data to Neumann data for a a general resistor network and explain how
the question of existence of a maximal resistor network comes about.
I then describe several maximal resistor networks, and show how the
resistors in these networks are recoverable from their Dirichlet to
Neumann maps.

2. General Resistor Networks

3. Maximal Resistor Networks