Exam 20: Graphs

In a(n)_______________ graph. if ,then so

The ____________________ traversal of a graph is similar to traversing a binary tree level by level.

In a graph directed G,for each vertex,v,the vertices adjacent to v are called ____ successors.

A tree T is called a(n)____________________ of graph G if T is a subgraph of G such that V(T )= V(G).

The depth first traversal is similar to the postorder traversal of a binary tree.

In Prim's algorithm for the minimal spanning tree,we start at a designated vertex,which we call the ____ vertex.

The two most common graph traversal algorithms are depth first traversal and breadth first traversal.

In a directed graph,the pairs (u,v)and (v,u)represent the same edge.

The shortest path is the path with the smallest ____.

Graph theory started in 1736 with the ____ problem.

A tree T is called a(n)____ tree of graph G if T is a subgraph of G such that V(T)= V(G); that is,if all vertices of G are in T.

Let G be a weighted graph.Let u and v be two vertices in G,and let P be a path in G from u to v.The weight of the path P is the sum of the weights of all the ____________________ on the path P.

Let G be an undirected graph.Let u and v be two vertices in G.A(n)____________________ in G is a simple path in which the first and last vertices are the same.

The ____ of sets A and B is the set of all elements that are in A and B.

Two well-known algorithms,Prim's algorithm and ____'s algorithm,can be used to find a minimal spanning tree of a graph.

If two edges,e? and e?,are associated with the same pair of vertices {u,v},then e? and e? are called ____ edges.

In a(n)____ graph,the edges are drawn using arrows.

A graph is called a(n)____ graph if it has no loops and no parallel edges.

The shortest path algorithm is also called the ____ algorithm.

The implementation of a breadth first graph traversal uses a stack.