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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:

enter image description here

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I have tried to improve the readability of your question by introducing Tex. It is possible that I unintentionally changed the meaning of your question. Please proofread the question to ensure this has not happened. –  A.P. Apr 17 '13 at 10:53
@A.P: its look fine now. thanks –  niro Apr 18 '13 at 1:22

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