Exam 20: Graphs

The ____________________ algorithm gives the shortest distance for a given node to every other node in the graph.

The edges connecting two vertices can be assigned a non-negative real number,called the ____ of the edge.

Let e (u,v)be an edge in an undirected graph G.The edge e is said to be ____________________ on the vertices u and v.

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

If the elements of E(G)are ordered pairs,G is called a(n)____ graph.

A maximal subset of connected vertices is called a ____ of G.

-A(n)____________________ ordering of the vertices of the accompanying graph is 0,1,4,3,2,5,7,8,6,9.

A graph is ____________________ if the number of vertices is zero.

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

A simple path is a path in which all vertices,except possibly the first and last vertices,are distinct.

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

The shortest path algorithm was developed by ____.

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

A set Y is called a(n)____________________ of X if every element of Y is also an element of X.

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.

We can always traverse an entire graph from a single vertex.

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

A graph might have cycles; therefore,we might not be able to traverse the entire graph from a single vertex.

The starting vertex of a shortest path in a graph is called the ____________________.

-A(n)____________________ ordering of the vertices of the accompanying graph is 0,1,3,4,2,5,7,8,6,9.