If I am having cycle graphs for example $G_1, G_2, G_3$. then how can I phrase union and intersection of adjoining graphs (i.e. having at least one common node with other) 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 $G_2 \cap G_3$.
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: