$\begingroup$

I have following definitions in my Graph Theory lecture notes:

1. The components of a graph G are its maximal connected subgraphs
2. A component (or graph) is trivial if it has no edges
3. An isolated vertex is a vertex of degree 0

What is the difference between a trivial component and an isolated vertex? I think they are equal. Is it true?

$\endgroup$

1 Answer

$\begingroup$

Yes you're right. A trivial component is a connected graph with no edges so it has degree 0 and is thus an isolated vertex. However. A trivial graph is the complement of $K_n$ and that is probably what the (graph) part under 2. wants to emphasize.

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

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