Question

In a directed graph, what defines a vertex as a global destination?

Option a) Presence of a Hamiltonian path
Option b) Existence of a path to every other vertex
Option c) Maximum indegree among all vertices
Option d) Minimum outdegree among all vertices

Answer 1

In a directed graph, a vertex is a global destination if there is a path from every other vertex to it, which is option b) Existence of a path to every other vertex.

Step-by-step explanation:

In a directed graph, a vertex is defined as a global destination if there exists a path from every other vertex in the graph to this particular vertex. Hence, the correct answer to what defines a vertex as a global destination is option b) Existence of a path to every other vertex.

This definition is not about having the maximum indegree or having the minimum outdegree; nor is it related to Hamiltonian paths. A global destination means that any other vertex can reach this specific vertex, regardless of how many edges enter it (indegree) or how many edges emerge from it (outdegree).