A Quicker Solution is
* Degree Sequence of Option A and C are not as same as the Given Graph. So can be eliminated
* In Option D vertex with degree 4 is adjacent to vertices with degrees {2,2,2,2} whereas in the given graph it is (vertex with degree 4) adjacent to vertices with degrees {1,2,2,2 } so option D can also be eliminated.
* Option B satisfies all necessary conditions and also also has a one to one corresspondence with the given graph.