doubt about my last question

Question

I have a very basic doubt. If we talk about rooted graph, can we consider any graph whose one vertex is labeled in a special way to distinguished it from other vertices or only rooted tree. this doubt is about my last question to clear doubt about basic definition in graph theory.

Here in the definiton can we take any graph like cycles, or complete graphs or only rooted tress. Thanks a lot for help.

score 3 · Accepted Answer · answered Aug 19 '13 at 04:13

3

We can indeed consider any graph with one vertex singled out as the root; for more information on rooted graphs you could start here. Rooted trees are merely a special case of rooted graphs in general.

answered Aug 19 '13 at 04:13

Brian M. Scott

616,228

Thanks a lot sir. I was very confused. Thanks – monalisa Aug 19 '13 at 04:16
@monalisa: You’re welcome! – Brian M. Scott Aug 19 '13 at 04:18
can we start this product after takin |V($G_n$)|=1? – monalisa Aug 19 '13 at 04:37
@monalisa: Are you asking whether we can form the hierarchical product when $G_n$ has only one vertex? Yes, though a factor with only one vertex doesn’t do much. – Brian M. Scott Aug 19 '13 at 04:46
yes sir, I am asking the same. I mean $G_n$ wit h only one vertex – monalisa Aug 19 '13 at 04:52
1

@monalisa: Yes, it’s possible. But if $G_2$ has only one vertex, then $G_2\sqcap G_1$ is isomorphic to $G_1$. – Brian M. Scott Aug 19 '13 at 04:55

doubt about my last question

1 Answers1