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4 numbered balls placed in 4 sites, two of one kind, and one of another.

Hi. The thing is that I was trying to find the number of graphs with the same topological structure. I was considering a particular graph, of 4 particles, connected by three lines, the first one in the picture. Because the book says so, I know there are 12 ways of ordering those particles with the same topological structure (look at the attached picture). Now, I was trying to make the counting in a statistical ground. I have four particles, wich I can put in four different places, but those places are not all equal. Some connects to two other particles, and some only connects to one particle.

http://mathhelpforum.com/attachments...ther-graph.png

Can somebody help me to do the counting?

Thanks in advance.