Using an argument involving paths determine which of the fol

Using an argument involving paths, determine which of the following graphs is not isomorphic to the other two.

Solution

First and third graphs are isomorphic to each other as there is a clear edge preserving bijection between the two graphs.

The second graph is not isomorphic to first and third because the vertex with degree three has a leaf attached directly to it in second graph however in first and third graphs, the leaf is not directy attached to the vertex of degree 3.