Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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:

enter image description here

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.

share|improve this question
add comment

1 Answer 1

Is this what you were looking for:

$G_1$ is a graph with vertex set $\{1,2,3\}$ and edge set $\{\{1,2\},\{1,3\},\{2,3\}\}$.

$G_2$ is a graph with vertex set $\{2,3,5,6\}$ and edge set $\{\{2,3\},\{3,5\},\{5,6\},\{2,6\}\}$.

So $G_1\cup G_2$ is a graph with vertex set $\{1,2,3,5,6\}$ and edge set $\{\{1,2\},\{1,3\},\{2,3\},\{3,5\},\{5,6\},\{2,6\}\}$. As you can see, I have simply taken the union of the vertex and the edge sets. Similarly $G_1\cap G_2$ is a graph with vertex set $\{2,3\}$ and edge set $\{\{2,3\}\}$. Here I have taken the intersections of the vertex and edge sets. All the others are obtained on similar lines.

share|improve this answer
    
@: thanks for the answer. but i am looking for something like below phrsing. not a simple list of nodes. math.stackexchange.com/questions/251396/amalgamation-of-graphs –  niro Apr 20 '13 at 12:58
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.