Let G be the graph v1 v2 e2 e1 and consider the walk v1e1v2e2v1. a. Can this walk be written unambiguously as v1v2v1? Why? b. Can this walk be written unambiguously as e1e2? Why? 4. Consider the following graph. v1 v2 v3 v4 e2 e1 e5 e3 e4 a. How many paths are there from v1 to v4? b. How many trails are there from v1 to v4? c. How many walks are there from v1 to v4? 5. Consider the following graph. e2 e1 e5 e3 e4 a c b a. How many paths are there from a to c? b. How many trails are there from a to c? c. How many walks are there from a to c? 6. An edge whose removal disconnects the graph of which it is a part is called a bridge. Find all bridges for each of the following graphs. a. v1 v5 v2 v4 v3 b. v0 v1 v2 v7 v8 v3 v4 v5 v6 c. v1 v9 v2 v3 v4 v5 v6 v7 v8 v10 7. Given any positive integer n, (a) find a connected graph with n edges such that removal of just one edge disconnects the graph; (b) find a connected graph with n edges that cannot be disconnected by the removal of any single e

MA 373 NOTES Noninterest Theory Facts 1. Sum of an Arithmetic Sequence = ((1 Term + Last Term) / 2) * (# of terms) Ex. 4 + 7 + 10 + 13 + 16 + 19 = ((4 + 19) / 2) * (6) = 69 2. Sum of Geometric Series = (First Term – Next Term after the last term) / (1 Ratio)...