I am asked to find the union of two cycle graph.
Union of $C_3$ and $C_5$ and union of $C_4$ and $C_4$.
Can anyone give me some hints on how to find it?
Does union of $C_4$ and $C_4$ actually mean combining the two square together such as that it is a new graph with 6 vertics and 6 edges?
And what about union of $C_3$ and $C_5$?
Thanks a lot
Generally, union of graphs means disjoint union, where for graphs $G_1 = (V_1,E_1)$ and $G_2 = (V_2,E_2)$, $G_1 \cup G_2 = (V_1 \cup V_2, E_1 \cup E_2)$ without considering whether graphs have some mutual nodes/edges or not. This means $C_4 \cup C_4$ is simply a disconnected graph with two $C_4$ components. So it has $8$ vertices and $8$ edges.
If it is not used in the meaning of disjoint union, then the result depends on vertex and edge set of the graphs. However, the definition $G_1 \cup G_2 = (V_1 \cup V_2, E_1 \cup E_2)$ remains the same.
EDIT FOR AN EXAMPLE: Take $G_1 = (V_1,E_1)$ and $G_2 = (V_2,E_2)$ where $G_1 \cong G_2 \cong C_4$ ($\cong$ states that they are isomorphic to $C_4$, I used that because I will enumerate vertices of $C_4$'s differently) where $$V_1 = \{v_1,v_2,v_3,v_4\}, E_1 = \{v_1v_2,v_2v_3,v_3v_4,v_4v_1\}$$ and $$V_2 = \{v_1,v_2,v_5,v_6\}, E_2 = \{v_1v_2,v_2v_5,v_5v_6,v_6v_1\}$$ Then, $G_1 \cup G_2 = (V_1 \cup V_2, E_1 \cup E_2)$ is the following graph:
So in your question, since it is not specified, I assumed it is disjoint union. If that is not the case, let me know so that I can edit my answer accordingly.