- #1

roadrunner

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## Homework Statement

Let G be a simple, connected d-regular graph and let A be its adjacency matrix.

(i) Show that A has largest eigenvalue d

(ii) Show that A has an eigenvalue of -d if and only if G is bipartite.

## Homework Equations

Don't know?

## The Attempt at a Solution

I really have no idea where to start with this one. It has been a LONG time since I dealt with eigenvalues.

Some direction or insight would be great!

I know that means I need to show that "No eigenvalue of a graph can exceed its maximum degree." I know that is true, I don't know how to show it.

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