-2
$\begingroup$

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.

Every 1-degree vertex must be connected to some another $>1$-degree vertex(if graph not connected then solution in the picture)enter image description here

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.

Thank you.

$\endgroup$
0
$\begingroup$

The degree sequence implies that there are $11$ vertices and $10$ edges. A connected graph with $n$ vertices and $n-1$ edges is a tree and therefore is acyclic. Thus, there is no unicyclic graph with the given degree sequence.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.