I have got graph $G$ and graph $H$.
My question is are these graphs isomorphic?
I think no, because in graph $G$ vertex $v_{2}$ has four neighbours:
- $v_{1}$ with degree two
- $v_{8}$ with degree three
- $v_{3}$ with degree four
- $v_{6}$ with degree five
But in graph $H$ vertex $x_{8}$ or $x_{4}$ has four neighbours but with different degrees.
For example $x_{8}$ has neighbours:
- $x_{9}$ with degree two
- $x_{1}$ with degree five
- $x_{4}$ with degree four
- $x_{7}$ with degree two
and $x_{4}$ has neighbours:
- $x_{3}$ with degree two
- $x_{1}$ with degree five
- $x_{8}$ with degree four
- $x_{5}$ with degree two
Because only $x_{4}$ and $x_{8}$ have degree four, not any one can be relfect to $v_{2}$ and $v_{3}$
So graphs $G$ and $H$ is non-isomorphic.
Is it correct please?