# Interpretation on the meaning of some graph theory statements

1. Nov 11, 2012

### Ceci020

Hello everyone,

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"

==> 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"

==> 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 --> B and A --> C but B --> D and C --> D and E --> 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"

==> Is this statement saying something about the "diagonal" ? Because I'm thinking about a picture of 4 vertices A, B, C, D
where A --> B and B --> C and C --> D. So A and D have degree at most 2 when I connect C with A and B with D.