Finding the eigenvalue for a given graph

[Falnom]

I'm having trouble finding the eigenvalue for a given graph; but more specifically I can't seem to find the characteristic polynomial. My book tells me that the characteristic polynomial of a simple graph with n vertices is the determinant of the matrix (A-\lambdaI), where A is the adjaceny matrix and I is the n X n identity matrix. What is \lambda? And I've read someplace else that the characteristic equation of a matrix is the determinant of (xI-A) - which is right, or are they both?
And isn't the root of the equation the eigenvalue?

 

[matt grime]

lambda is a variable, use x if you prefer. It's just a letter.

 

[Falnom]

Ah yes of course, I had thought as much. Thank you very much. (It works now!)