gr-t1

# 6 5 pts sketch a graph g that has the following

This preview shows pages 3–4. Sign up to view the full content.

6. (5 pts.) Sketch a graph G that has the following adjacency matrix: A G 010110 101001 010100 101010 100101 010010

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
TEST1/MAD3305 Page 4 of 4 _________________________________________________________________ 7. (5 pts.) Construct a 3-regular graph G of minimum order that contains C 4 as an induced subgraph. [Use the ideas of Paul Erdos and Paul J. Kelly.] _________________________________________________________________ 8. (10 pts.) Prove exactly one of the following propositions. Indicate clearly which you are demonstrating. (a) If G is a non-trivial graph, then there are distinct vertices u and v in G with deg(u) = deg(v). (b) If G is a graph of order n and deg(u) + deg(v) n-1f o r each pair of non-adjacent vertices u and v, then G is connected. _________________________________________________________________ 9. (10 pts.) (a) Suppose G is a bipartite graph of order at least 5. Prove that the complement of G is not bipartite. [Hint: At least one partite set has three elements. Connect the dots?] (b) Display a bipartite graph G of order 4 and its bipartite complement.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page3 / 4

6 5 pts Sketch a graph G that has the following adjacency...

This preview shows document pages 3 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online