Daily Anything

Replies

Mar 14, 2019 7 years ago

Before you die, you see

Oh fer cryin out loud

<3 Lead with Love. Try to understand instead of trying to be right. <3 Stylefile WL search here for holiday trades

Mar 14, 2019 7 years ago

is forever alone

vecwxt

"The theory of the multiverse says there are
infinite parallel universes containing every possible situation.
It makes me happy, because I know, somewhere, you love me back."

Mar 15, 2019 7 years ago

is a demon

anything

Mar 16, 2019 7 years ago

the snuggle monster

anything anything

[center][center]

Mar 16, 2019 7 years ago

is a demon

nothing

Mar 16, 2019 7 years ago

is getting bi

something

[flower=vantula]

Mar 16, 2019 7 years ago

is a demon

Something

Mar 21, 2019 7 years ago

is buggin out

Anything

• they/it •

• wishlist •

[kiss/=smallcritter]

[dance/=smallcritter]

[tot/=smallcritter]

[tree/=smallcritter]

Mar 29, 2019 7 years ago

is a demon

Nothing

Mar 29, 2019 7 years ago

made a huge mistake

What I'm working on IRL

item textbf{Definition:} Let $G$ be any graph. We'll define the textbf{complement} of $G$ (and write $overline{G}$) to be the graph with $V(overline{G}) = V(G)$ (i.e., both graphs have the same set of vertices), but $ab$ is in $E(overline{G})$ if and only if $ab$ is emph{not} in $E(G)$.


begin{enumerate}
item Let $G$ be the graph shown on the left.  Using the vertices on the right, draw $overline{G}$. vspace*{0.2in}
begin{tikzpicture}
   filldraw (30:1) circle (2pt);
   filldraw (90:1) circle (2pt);
   filldraw (150:1) circle (2pt);
   filldraw (210:1) circle (2pt);
   filldraw (270:1) circle (2pt);
   filldraw (330:1) circle (2pt);
   draw (30:1) -- (90:1) -- (150:1) -- (210:1) -- (270:1) -- (330:1) -- (30:1);
end{tikzpicture} hspace{2in}
begin{tikzpicture}
   filldraw (30:1) circle (2pt);
   filldraw (90:1) circle (2pt);
   filldraw (150:1) circle (2pt);
   filldraw (210:1) circle (2pt);
   filldraw (270:1) circle (2pt);
   filldraw (330:1) circle (2pt);
   draw[black!30,loosely dotted] (30:1) -- (90:1) -- (150:1) -- (210:1) -- (270:1) -- (330:1) -- (30:1);
end{tikzpicture}

vfill 

item Prove that if $G$ has six vertices, then $G$ and $overline{G}$ cannot both be bipartite.

vfill

end{enumerate}