# Finding the eigenvalue for a given graph

1. Dec 8, 2004

### 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-$$\lambda$$I), 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?

2. Dec 8, 2004

### matt grime

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

3. Dec 8, 2004

### Falnom

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