---
# System prepended metadata

title: Assignment 1
tags: [Assignments]

---

---
tags: Assignments
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# Assignment 1

:::info
Due Friday August 12.
:::

```graphviz
graph question1{ 
{ rank = same; 
node [shape=circle]
1 [label="A"]
2 [label="B"]
3 [label="C"] 
1 -- 2 -- 3 }
}
```

1. Calculate by hand the spectrum of the graph above. Show all of your working. **(3 marks)**
2. Let $\Delta$ be the maximum degree of any vertex in a connected graph $\Gamma$. Prove that $\Gamma$ is regular if and only if $\Delta$ is an eigenvalue of $\Gamma$. **(6 marks)**
3. Show that no graph has eigenvalue $-1/2$. **(6 marks)**