HelpNeeder
New member
- Joined
- Feb 17, 2021
- Messages
- 33
These are true/false question I'm trying to solve to prepare for my exam. Could someone please confirm my answers or help me to get the correct ones?
a) a graph in which each vertex has the same number of vertices at a distance of 2 is always regular
I think:
True, because if each vertex has the same number of vertices at a distance of 2, then it has the same number of vertices at distance one, so it is regular.
b) every bipartite Eulerian graph has an even amount of edges
I think: false, but I cannot come up with an example to prove my statement.
c) There are exactly 2 23-regular graphs with 25 vertices.
I think: false, there is none. The sum of the degrees needs to be even, but 23 * 25 is odd.
a) a graph in which each vertex has the same number of vertices at a distance of 2 is always regular
I think:
True, because if each vertex has the same number of vertices at a distance of 2, then it has the same number of vertices at distance one, so it is regular.
b) every bipartite Eulerian graph has an even amount of edges
I think: false, but I cannot come up with an example to prove my statement.
c) There are exactly 2 23-regular graphs with 25 vertices.
I think: false, there is none. The sum of the degrees needs to be even, but 23 * 25 is odd.
