I am learning about regular graphs and have found that there are only 5 different options for a simple connected 3-regular graph with 8 vertices (source: http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html).
However, when I start plotting option for myself, I find it often very hard to determine whether two graphs are isomorphic or not. Here is an example with the first five graphs depicting the five options given in the link above and the sixth one of my additions:
Best Answer
The new option is equivalent to option 1. I found this by looking for cycles in the graph and checking in what way the cycles are attached to one another: you have four 3-cycles; two pairs of the four 3-cycles share an edge and then there are two edges (23 and 67 in Option 1) that connect everything.