What is $\langle I\rangle$ in this text?

66 Views Asked by At

I've read the following:

It is easy to see that given any independent set $I$ in $V$, the vertices of $V-I$ form a covering of $G$. Conversely, if $V-I$ forms a covering, then $\langle I\rangle$ must be empty; hence, it must be independent.

What is $\langle I\rangle$? I tried to search for it in the book I'm reading but couldn't. It doesn't have a notational index.

1

There are 1 best solutions below

2
On BEST ANSWER

The comments by user66081 and Manuel Lafond are correct; $\langle I \rangle$ refers to the subgraph of $G$ induced by $I$. In Gould's Graph Theory, the notation is introduced on page 6:

Given a subset $S$ of $V(G)$, the subgraph induced by $S$, denoted $\langle S \rangle$, is that graph with vertex set $S$ and edge set consisting of those edges of $G$ incident with two vertices of $S$.