In: Advanced Math
Problem 2. Consider a graph G = (V,E) where |V|=n.
2(a) What is the total number of possible paths of length k ≥ 0 in G from a given starting vertex s and ending vertex t? Hint: a path of length k is a sequence of k + 1 vertices without duplicates.
2(b) What is the total number of possible paths of any length in G from a given starting vertex s and ending vertex t?
2(c) What is the total number of possible cycles of any length in G from a given starting vertex s?
Problem 2. Consider a graph G = (V,E) where |V|=n.
2(a) What is the total number of possible paths of length k ≥ 0 in G from a given starting vertex s and ending vertex t? Hint: a path of length k is a sequence of k + 1 vertices without duplicates.
2(b) What is the total number of possible paths of any length in G from a given starting vertex s and ending vertex t?
2(c) What is the total number of possible cycles of any length in G from a given starting vertex s?