can anyone phrase a common definition for the union and intersection for below case.
Actually I am looking for mathematical expression in mathematical notations.
For example if I want to do $G_1 \cup G_2$ or $G_2 \cup G_3$ and $G1 \cap G_2$ or $G_2 \cap G_3$. (*As I feel, the situation is different because one edge and one node is common for (G1, G2) and (G2,G3) respectively)
So, I want to phrase these intersection and union with common variables with mathematical notations (except $G_1, G_2, G_3$).
Here, is my example figure:
NOTE: I am looking for some mathematical phrasing. for example in Amalgamation of graphs, in the answer, it uses different notation. So, looking for similar phrasing.