I'm reviewing previous exams of Graph Theory and found this question:

Consider a strongly connected directed graph G and its underlying undirected graph G*. Prove that λ(G*) ≥ 2.

But I am confused. How can a directed graph have an undirected subgraph? Doesn't "digraph" imply that all edges are directed?

  • 1
    $\begingroup$ In $G^*$ you just 'forget' the direction. $\endgroup$ – Leen Droogendijk May 23 '14 at 17:24

The "underlying undirected graph," $~G^*$, is just $G$ without the edges having any direction. Since $G$ is strongly connected, every pair of vertices in $G^*$ lies on some cycle in $G^*$. Hence deleting a single edge cannot disconnect the graph. Therefore $\lambda(G^*)\geq2$.


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.