Science:Math Exam Resources/Courses/MATH307/April 2012/Question 04 (e)/Statement

Consider a network arranged in the shape of an octahedron as in this diagram:

The nodes have been labeled with the large numbers and 3 of the edges (resistors) have been given orientations and labeled with small numbers. Assume all resistances are equal to 1. Let D be the incidence matrix (for some choice of labeling and arrows for the remaining edges) and let L be the Laplacian.

(e) It seems reasonable to conjecture that the effective resistance between nodes 1 and 6 would remain unchanged if removed the resistors between 2 and 3, 3 and 4, 4 and 5, 5 and 2. Explain how you could use MATLAB/Octave to test this conjecture. Assume that L has been defined in MATLAB/Octave.