Answer True or False to the following claims: a. Let G be a connected graph on 42 vertices and G contains exactly one cycle.   The G must contain exactly 42 edges.   b. There exists a graph on 42 vertices in which every path has length at most 2. (Recall that a path is not permitted to use the same edge twice in a row.)   c. Let G1 be a graph on 5 vertices and 9 edges. Let G2 be a graph on 5 vertices and 9 edges. Then G1 and G2 are necessarily isomorphic.

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Answer True or False to the following claims:

a. Let G be a connected graph on 42 vertices and G contains exactly one cycle.  

The G must contain exactly 42 edges.

 

b. There exists a graph on 42 vertices in which every path has length at most 2.

(Recall that a path is not permitted to use the same edge twice in a row.)

 

c. Let G1 be a graph on 5 vertices and 9 edges.
Let G2 be a graph on 5 vertices and 9 edges.
Then G1 and G2 are necessarily isomorphic.

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