Exam 20: Graph Algorithms

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

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

A(n) ____ tree T is a simple graph such that if u and v are two vertices in T, a unique path exists from u to v.

Let G be an undirected graph.Let u and v be two vertices in G.Then u and v are called ____ if there is an edge from one to the other.

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

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

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

The shortest path algorithm was developed by ____.

The shortest path algorithm is also called the ____ algorithm.

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

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.

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

____________________ algorithm builds the tree iteratively by adding edges until a minimal spanning tree is obtained.

A binary tree has no cycles.

In a(n) ____________________ graph, the tail of a pictorial directed edge is the origin, and the head is the destination.

It is possible to design Prim's algorithm so that it is of the order O(n²).

An edge incident on a single vertex is called a(n) ____.

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.

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

Y is a(n) ____ of X if every element of Y is also an element of X.