1
$\begingroup$

I know that a graph G' is a subgraph for G if V(G')⊆V(G) and E(G')⊆E(G).

Today my professor wrote that G' is a subgraph for G if G' is a graph and V(G')⊆V(G), and then he told us that this definition is equivalent to the one we've seen before (= the first line in this post).

However, I don't think that these definitions are equivalent. In fact, if this is G:

       2
     /   \
    1     3

and this is G':

    1 - 3

we have that G' is a subgraph for G according to the second definition (wrong), while it is not according to the first one (right).

Am I missing something or was the professor wrong?

$\endgroup$
2
$\begingroup$

The alternative definition that you attribute to your professor is wrong, as your counterexample clearly shows.

I hope your professor actually said something else and you misunderstood him/her!

$\endgroup$

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.