gr-t1 - NAME TEST1/MAD3305 Page 1 of 4 General directions...

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NAME: TEST1/MAD3305 Page 1 of 4 _________________________________________________________________ General directions: Read each problem carefully and do exactly what is requested. Show all your work neatly. Use complete sentences and use notation correctly. Make your arguments and proofs as complete as possible. Remember that what is illegible or incomprehensible is worthless. Show me all the magic on the page. _________________________________________________________________ 1. (25 pts.) Provide brief answers to each of the following: (a) What is the order and size of the graph K 9,13 ?? Say which is which unequivocally. (b) The degree of each vertex of a certain graph of order 12 and size 31 is either 4 or 6. How many vertices of degree 6 are there? (c) Suppose G is a connected non-trivial graph and u and v are two vertices with d(u,v) = 47. What is the order of the smallest connected subgraph H of G that contains u and v? What can you say about the diameter of G? (d) Suppose that G is a graph of order 25 and size 99. From this information, we know that any trail in G can be no longer than what number l? Provide the best upper bound.
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