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{\bf MATH314  \hspace{1cm} HW 2\hfill \name}
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Due \textbf{Feb 4} before class, \textbf{answer without justification will receive 0 points}.
The typing the HW in \LaTeX{} is optional. 
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\question{3.2}{
Give an example of three graphs of the same order, same size and same degree sequence such that no two of these graphs are isomorphic.
}

\textbf{Solution:}

\question{3.10}{
Does there exist a disconnected self-complementary graph?
}

\textbf{Solution:}

\question{3.12}{
Let $G$ and $H$ be two self-complementary graphs with disjoint vertex sets, where $H$ has even order $n$. Let $F$ be the graph obtained from $G\cup H$ by joining each vertex of $G$ to every vertex of degree less than $n/2$ in $H$. Show that $F$ is self-complementary.
(No drawing)
}

\textbf{Solution:}

\question{3.16}{
How many (non-isomorphic) graphs have the degree sequence s: 6, 6, 6, 6, 6, 6, 6, 6, 6?
}

\textbf{Solution:}

\question{}{
Count the number of automorphisms (that is isomorphism to itself) of the Petersen graph.
}

\textbf{Solution:}

\question{}{
Let $A$ be the adjacency matrix of a graph $G$, where $G$ is a triangle-free graph (that is, no $K_3$ as a subgraph). 
What are entries of the diagonal  of $A^3$?  (No drawing)
}

\textbf{Solution:}






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