Graph Theory Lessons

Answers to Lesson 14

  1. Kn+ N1 is isomorphic to Kn + 1.

  2. Nr + N1 is isomorphic to Sr + 1. It is also isomorphic to the complete bipartite graph K1,r. and to the full r-ary tree with one level and also to the star Sr+1.

  3. Nr + Ns is isomorpic to the complete bipartite graph Kr,s.

  4. Nr U Ns is isomorpic to the null graph Nr + s.

  5. Nr + Ns + Nt is isomorpic to the complete tripartite graph Kr, s, t.

  6. Cn + N1 is isomorpic to the wheel Wn + 1.

  7. If X(G1)=a and X(G2)=b, then X(G1 U G2) = max{a, b}.

  8. If X(G1)=a and X(G2)=b, then X(G1 + G2) = a + b.
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