In the following figure I tried to draw a graph from $P_{11}$ (vertex set as $u_1,\ldots,u_{11}$) by adding two vertices(red colored) to $P_{11}$, with exactly two vertices having eccentricity five and rest of the vertices having eccentricity four. I want the resultant graph to an induced subgraph of $P_{11}$.
I almost succeeded but unable to move forward from here. I want eccentricity of $u_1$ and $y$ to be fourKindly help. Thanks a lot for the help.
Note: Eccentricity of vertices is given in numbers.
Is there any other way to make $P_{11}$ as induced subgraph of a graph $G$, Eccentricity of every vertex is four and two vertices have acc 5. $G$ is obtained by adding two vertices to $P_{11}$.