I want to find some example unicyclic graph with degree sequence $(4,3,3,2,2,1,1,1,1,1,1)$.
I think that this graph not exists.
We need to use $\ge 4$ edges in cycle and edge for connected to some another $>1$-degree.
Every $>1$-degree vertex must be connected to another $>1$ too.
$\ge 4$ edges in cycles, $1$ edge for connected cyclic to another and for $>1$ vertices.
But i dont undestand that i need do later.