I ran into a question in my textbook asking how many non-isomorphic simple graphs are there with 5 vertices and 3 edges, the answer says its 4, but I have no idea how I'm supposed to get that, there are also no examples of anything like this question either, I'm studying this for a midterm so I am much more interested in the process than the answer.
So I have a couple of confusions with this question. I tried to draw some graphs with v=5 and e=3 but stopped after like 3 after realizing there are so many graphs that are possible, am I really supposed to go through every single one and see if its isomorphic or not? also what am I even supposed check if its isomorphic to? I thought you needed 2 graphs to determine if they are isomorphic, What does it even mean to determine if one graph is isomorphic or not? Even when you have the 2 graphs you need to do a series of steps to check if they are even isomorphic right? The method we use right now is to check for equal edges, vertices, and series of degrees, and then we try to map each vertex to one on the other graph, if everything works it's isomorphic. Which in this case seems like it will take a very long time to do for all the possibilities. I don't think this question is supposed to be nearly as hard as I perceived. What am I missing here?
Furthermore how would I do this for other questions like this? for example 4 edges, 5 edges, 6 vertices, 7 vertices, etc. is there a series of steps I'm supposed to follow to solve a question like this?