I'm studying basic graph theory, and my instructor gives me these statements to translate into pictures. I don't quite understand the meanings of the statements, but I have some thoughts about them.
1/ "Any two vertices a, b are connected by at least 2 distinct paths of length 4"
$\Longrightarrow$ Does this mean that any two vertices $a$, $b$ are connected by at least 1 path of length 8?
2/ "Any vertex of degree 2 is connected by a path of length 3 with a vertex of degree 3" $\Longrightarrow$ what does this mean ? (in terms of a picture)
I'm thinking about a picture of 5 vertices $A$, $B$, $C$, $D$, $E$, where $A \longrightarrow B$ and $A \longrightarrow C$ but $B \longrightarrow D$ and $C \longrightarrow D$ and $E \longrightarrow D$ and $E$ doesn't connect with $A$. Is this idea right ?
3/ " Any 2 vertices connected by a path of length 3 have degree at most 2"
$\Longrightarrow$ Is this statement saying something about the "diagonal" ? Because I'm thinking about a picture of 4 vertices $A$, $B$, $C$, $D$ where $A \longrightarrow B$ and $B \longrightarrow C$ and $C \longrightarrow D$. So $A$ and $D$ have degree at most 2 when I connect $C$ with $A$ and $B$ with $D$.
Would you please help me on these questions? Thank you in advance. :)