Exam 12: Graphs

Let V(G) denote the set of vertices, and E(G) denote the set of edges of a graph G, then if the elements of E are ordered pairs, G is called a directed graph or ____.

A weight free tree T is a simple graph such that if u and v are two vertices in T, there is a unique path from u to v.

A ____ is a path of nonzero length from a vertex u to u with no repeated edges.

The shortest path algorithm, also called a greedy algorithm, was developed by Dijkstra.

How a graph is represented in computer memory depends on the specific application.

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

Traversing a graph is different than traversing a binary tree.

In the breadth first traversal algorithm, the root node is visited last.

In 1736, Euler represented the Königsberg bridge problem as a graph, marking (as recorded) the birth of graph theory.

To write programs that process and manipulate graphs, the graphs must be stored in computer memory.

In the breadth first traversal of a graph, all the nodes at any level, i, are visited after visiting the nodes at level i + 1.

Let G be an undirected graph. A maximal subset of connected vertices is called a ____ of G.

The symbol ''____'' means ''Cartesian product.''

A graph is empty if the number of vertices is 1.

In a directed graph, the edges are drawn using ____.

In an undirected graph, the edges are drawn using ____.

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

A graph G has a spanning tree if and only if G is connected; from this it follows that to determine a spanning tree of a graph, the graph must be connected.

The breadth first traversal of a graph is similar to traversing a binary tree ____.

In breadth first traversal, starting at the first vertex, the graph is traversed as little as possible.