Question

Let G be a directed graph whose vertex set is the set of numbers from 1 to 50. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. Calculate the minimum number of edges in a path in G from vertex 1 to vertex 50.

(a) 98

(b) 13

(c) 6

(d) 34

The question was asked by my college professor while I was bunking the class.

Question is from Complete and Connected Graphs topic in division Graphs of Discrete Mathematics

Answer 1

Right answer is (c) 6

Easiest explanation: Edge set consists of edges from i to j using either 1) j = i+1 OR 2) j=3i. The trick to solving this question is to think in a reverse way. Instead of finding a path from 1 to 50, try to find a path from 100 to 1. The edge sequence with the minimum number of edges is 1 – 3 – 9 – 10 – 11 – 33 which consists of 6 edges.