1
$\begingroup$

The center of a graph is the set of vertices with minimum eccentricity, so a $C_n$ have the minimum eccentricity equals to $n$ and a $K_n$ have the minimum eccentricity equals to $1$? Is valid that a center of a graph be the graph itself?

$\endgroup$

1 Answer 1

0
$\begingroup$

Let $G = (V, E)$ be a graph. If the eccentricity of each vertex $v \in V$ is $c$. Then the center of the graph is $V$, the set of all vertices of the graph $G$. Note that the center is the set $V$ of vertices not the graph $G$. In general the center of a graph $G = (V, E)$ is a subset of $V$.

$\endgroup$
1
  • 1
    $\begingroup$ It's very common, though informal, to say that some set of vertices is "the whole graph" if that set is $V(G)$. $\endgroup$ May 2, 2017 at 19:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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