1. ## isomorphism

Ans. two graphs are not isomorphism
Although their degree sequence is corresponding but
in graph(i) the vertex of degree2 is adjacency to two vertices of degree4,in graph(ii) the vertex of degree2 is adjacency to one vertice of degree1 and one vertice of degree4. therefore two graphs are not isomorphism.

2. in graph(i) the vertex of degree2 is adjacency to two vertices of degree4,in graph(ii) the vertex of degree2 is adjacency to one vertice of degree1 and one vertice of degree4.
Yes, with a small remark that there are two vertices of degree 2 in the first graph, not "the" vertex.

3. ans.
(i)no
(ii)1
(iii)3
(iv)6

I'm not sure.

4. I would say that there is one tree with three vertices. I believe you meant that there are no non-isomorphic trees with three vertices, but I think the question asks how many trees are there up to isomorphism.

For a list of threes with up to six vertices see Tree -- from Wolfram MathWorld.

5. 2. I can't
3.I think two graph is planar

graph theory is so difficult for me but I will try my best. -0-