I do not want to put two 'My' in the diagram ...
NOT A TEACHER
Krishnap, when you use the word "diagram," are you referring to the Reed-Kellogg system of diagramming? The one in which you draw vertical and horizontal lines? If you are, hopefully someone who knows that system will post the diagram. I know a little about that system, but I do not know how to post diagrams. So I shall just use words. Of course, a picture [diagram] is worth a thousand words.
1. You write the word "dog" on a short horizontal line.
2.
Under that horizontal line, draw another short horizontal line with "cat."
3. You connect those two horizontal lines with the word "and." (I assume that you know how to do that. I cannot explain how to do so in words.)
4. You then draw a long horizontal line. Under that line, you draw a short slanted line with the word "my" on it.
Congratulations on learning diagramming. Although almost all teachers nowadays think that the Reed-Kellogg diagramming system is a waste of time and does not help the student learn English, I respectfully disagree. (At the university, tree diagrams are used in linguistic classes.)