Doubt Perfext Matching

Question

Finda a graph with every vertex degree at least 2, and have only one perfext matching. (In Perfect matching all vertex are matched.)

Answer 1

Yes there are such graphs.

O--------O------------O

|        /             /  |

|      /            /     |

|   /            O------O

O

 

try to draw this graph and find perfect matching .:

Comments

Shall we generalize as two odd cycles sharing exactly one vertex have this property?? (i.e perfect matching)