Answer
(a) We can use a graph to model the layout of the city.
(b) Since the graph has exactly two odd vertices, the graph has at least one Euler path. By following an Euler path, it is possible to cross each bridge exactly once.
(c) A route which crosses each bridge exactly once should start at either Island A or Island B.
Work Step by Step
(a) We can use a graph to model the layout of the city. Each vertex represents one land mass and each edge represents a bridge between two land masses.
(b) We need to verify the number of odd vertices in the graph. Vertex Island A and vertex Island B are odd vertices. The other vertices are even. Since the graph has exactly two odd vertices, the graph has at least one Euler path.
An Euler path is a path which travels through every edge of the graph exactly once. Each edge in the graph represents a bridge. By following an Euler path, it would be possible to cross each bridge exactly once.
Since this graph has at least one Euler path, it is possible to find a path that crosses each bridge exactly once.
(c) When a graph has exactly two odd vertices, any Euler path starts at one odd vertex and ends at the other odd vertex. Therefore, a route which crosses each bridge exactly once should start at either Island A or Island B.
