gr-t1-a

# The sets u and w are called partite sets e diameter

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[The sets U and W are called partite sets.] (e) Diameter: The greatest distance between any two vertices of a connected graph G is called the diameter of G and is denoted diam(G). So diam(G) = max { d(u,v): u,v ε V(G) }. _________________________________________________________________ 3. (5 pts.) List the r-regular graphs of order 5 for all possible values of r. They are all old friends. The r-regular graphs of order 5 are the empty graph of order 5 w i t hr=0 ,t h e 5-cycle withr=2 ,a n dt h

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TEST1/MAD3305 Page 3 of 4 _________________________________________________________________ 4. (10 pts.) Use the Havel-Hakimi Theorem to construct a graph with degree sequence s: 7,5,4,4,4,3,2,1 s 1 : 4,3,3,3,2,1,0 s 2 : 2,2,2,1,1,0 s 3 : 1,1,1,1,0 [Graphic] _________________________________________________________________ 5. (10 pts.) Use the ideas from the proof of Theorem 2.7, to construct a 3-regular graph G that contains K 3 as an induced subgraph. Show each stage of the construction. _________________________________________________________________ 6. (5 pts.) Sketch a graph G that has the following adjacency matrix: A G 010110 101001 010100 101010 100101 010010
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.] Since δ (C 4 )=2a
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The sets U and W are called partite sets e Diameter The...

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