natural sub-class of trees in Sage

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I want to calculate certain parameter for class of trees like path graphs, star graphs. I dont want to calculate it for all trees with n vertices as this wont help me in my problem. Basically I need a natural class of trees.

I have found that path graph and star graph is available in sage.

If you can suggest me some other class of trees like this in sage it will be very helpful to me.

Thank you.