# Thread: What does this Graph look like?

1. ## What does this Graph look like?

Hello,

I'm doing a problem in which I have to find if a graph is Eulerian, Hamiltonian, and other thing like that. However, I don't know what this graph would look like.

(K2 U C3) x P3

K2 would look like this: *--*

C3 would be a triangle

So K2 U C3 would be: *--* [Triangle]

What does it look like when you cross these with a P3 (P3 looks like *--*--*)

2. This may surprise you, but there is no standard notation.
So I have no idea what those graphs are suppose to represent.
You have to define all you notation if you expect any help.

3. Originally Posted by Plato
This may surprise you, but there is no standard notation.
So I have no idea what those graphs are suppose to represent.
You have to define all you notation if you expect any help.

Okay, I'll try to help:

K2 is a complete graph of 2 vertices. A complete graph is a graph in which every two distinct vertices are joined by exactly one edge. The complete graph with n vertices is denoted by Kn.

C3 is a cycle of 3 vertices. The cycle graph with n vertices is denoted by Cn.

U means the "union" of the two. Which mean the two graphs are next too each other not connected at all. For two graphs with disjoint vertex sets V1 and V2 (and hence disjoint edge sets), their disjoint union is the graph U(V1 ∪ V2, E1 ∪ E2).[1] It is a commutative and associative operation (for unlabelled graphs).

X means Cartesian Product. The vertex set of G X H is the Cartesian product V(G) × V(H); and

any two vertices (u,u') and (v,v') are adjacent in G X H if and only if either

u = v and u' is adjacent with v' in H, or

u' = v' and u is adjacent with v in G.

This help?