title: Using DFS on a Graph - Determine if a graph is a clique with specific SCC
body: <p>I have a simple question on DFS and I'm trying to understand how to use it and not how to solve the whole problem. I'm really looking for an explanation and not a solution to my homework.</p>
  
  <p>I'll write down the question first.</p>
  
  <blockquote>
    <p>"Suppose you have an undirected graph G=(V,E) and let three of its
    vertices to be called v1, v2 and v3. Find an algorithm which
    determines if these three vertices are part of a clique
    (complete graph) (k>=3)"</p>
  </blockquote>
  
  <p>Now I suppose to use DFS in order to solve it. As far as I understand DFS will let me know if v1, v2 and v3 are in the same strongly connected component. If I'm correct I should also determine if G is  also a clique(complete graph).</p>
  
  <p>I read in the internet and I found out that asserting if a graph is clique or not is NP and cannot be solved easily. Am I correct? Am I missing anything? Is there any propery I can use to determine immediately if a graph is comeplete ?</p>