NL- definition and a problem
Hint: How much space do you need to store a set of $10$ vertices? How much space does it take to go over all pairs of nodes in a graph?

Another hint: How much space does it take to implement the following algorithm? (I replaced 10 with 3 to make it easier to follow)

 int algorithm(int n, int G[n][n]) {
   int x, y, flag;
   int v1, v2, v3;

   for (v1 = 0; v1 &lt; n; v1++)
     for (v2 = 0; v2 &lt; n; v2++)
       for (v3 = 0; v3 &lt; n; v3++) {
         flag = 0;
         for (x = 0; x &lt; n; x++)
           for (y = 0; y &lt; n; y++)
             if ((x != v1) &amp;&amp; (x != v2) &amp;&amp; (x != v3) &amp;&amp;
                 (y != v1) &amp;&amp; (y != v2) &amp;&amp; (y != v3))
               flag |= G[x][y];
         if (flag == 0)
           return 1;
       }
   return 0;
 }