Exam 20: Graph Algorithms

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

A graph G is a pair, G = (V, E), where V is a finite nonempty set called the set of ____ of G, and the elements of E are the pairs of elements of V.

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

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

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

In a graph G, if the edges connecting two vertices have weights assigned to them, the graph is called a ____ graph.

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

A minimal spanning tree of G is a spanning tree with the minimum ____.

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

If two edges, e₁ and e₂, are associated with the same pair of vertices {u, v}, then e₁ and e₂ are called ____ edges.

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

A tree in which a particular vertex is designated as a root is called a(n) ____ tree.

Linked lists cannot be used to implement an adjacency list.

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

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

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

A graph H is called a(n) ____ of G if V(H) is a subset of V(G) and E(H) is a subset of E(G); that is, every vertex of H is a vertex of G, and every edge in H is an edge in G.

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.

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

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