Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For a simple graph of 1 node/vertex with no edges (null graph), what would the complement of this graph be? Would it be a loop with itself or a null graph with one vertex? Or neither?


share|cite|improve this question
I think we keep the "simple" property of a graph under complementation. Hence, the complement of the simple graph, $G$, consisting of one vertex would be $G$ itself. – eeeeeeeeee Jan 13 '13 at 0:37
up vote 1 down vote accepted

It would be the same graph, since a simple graph cant have loops, and a complement graph has the same vertices as the original.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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