Science:Math Exam Resources/Courses/MATH307/April 2012/Question 04 (c)/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.

(c) Is is true that N(D) = N(L)? Give a reason.