Eigenvalues of adjacency matrices and row sums

[Niels]

I'm having an exam on graph theory next week and I'm having some problem with understanding the meaning of calculating eigenvalues of adjacency matrices for graphs. My notes suck from the lectures and I'm totally lost...

Our professor asked "What is the sum of elements in row k of the adjacency matrix?" and showed an example where he calculated the eigenvalues of $C_3$ (2, -1, -1) but then my notes stop and and I can't connect the eigenvalues to the question...

Any input on this subject most welcome... Any one know any good resource on the net where I can find more on this??

 

[Janitor]

I don't know of websites on that topic, though I don't doubt there are some.

Out of curiosity, in connection with your problem, are the graphs understood to be undirected? Can a node be adjacent to itself, i.e. are "loops" allowed in the type of graph you are talking about? I am pretty sure that different authors put different restrictions on the properties of a graph when defining that term.

 

[Niels]

The graphs are undirected without loops...

 

[Janitor]

I just found this website, which has some theorems involving eigenvalues:

http://www.cs.berkeley.edu/~demmel/cs267/lecture20/lecture20.html

Don't know if it will help with your particular issue.