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title: Assignment 2
tags: [Assignments]

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tags: Assignments
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# Assignment 2

:::info
Due Friday August 26
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1. Write the Krein conditions for a strongly regular graph with no triangles, in terms of $k$ and $\mu$. Simplify your answer as much as possible. **(3 marks)**
2. There are finitely many strongly regular graphs with parameters $(n,k,\lambda,\mu)$ where $\lambda=0$ and $\mu=1$. Find all possible values of $(n,k)$, and show all of your working. (_Hint:_ Show that $4k-3=s^2$ for some integer $s$, and then show that $s$ divides $15$). **(6 marks)**
3. Show that a $2$-design (with $v>k$) is symmetric (i.e., has the same number as points as blocks) if and only if there is a constant $C$ such that any two blocks intersect in $C$ points. **(6 marks)**