Nonisomorphic graphs Discrete Math

Find 3 different nonisomorphic graphs with 8 vertices that have the degree sequence 2,2,2,2,2,2,2,2. Answer: An 8-cycle, or two 4-cycles, or a 3-cycle and a 5-cycle.

Can someone show me how these three answers were found? I am a little confused with nonisomorphic graphs. I used to think you could just change the name of each vertex because no matter how you rearranged the vertices they would never be able to be rearranged back to their previous form. But then I was wrong and was told that you have to pay attention to adjacency but how? So for this question, how did the person come by these three answers?

Find 3 different nonisomorphic graphs with 8 vertices that have the degree sequence 2,2,2,2,2,2,2,2. Answer: An 8-cycle, or two 4-cycles, or a 3-cycle and a 5-cycle.

Can someone show me how these three answers were found? I am a little confused with nonisomorphic graphs. I used to think you could just change the name of each vertex because no matter how you rearranged the vertices they would never be able to be rearranged back to their previous form. But then I was wrong and was told that you have to pay attention to adjacency but how? So for this question, how did the person come by these three answers?