Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 201 05 (a)
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Question Section 201 05 (a) 

Consider the following graph, interpreted as a resistor network with all resistances R = 1. (a) Write down the incidence matrix D and the Laplacian matrix L for this graph. Show that (for any graph) N(L) = N(D). Is it true that R(D^{T}) = R(L)? Give a reason. 
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Hint 

Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 201 05 (a)/Hint 1 
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Solution 

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Answer: Reading off the graph (where 1 is info leaving node and +1 is info entering node):
and can either compute L by } L = D^TD \text{ or get it directly from the graph using the following method:
As for nullspaces of L and D,
Also:
