Exam 13: Sets and Maps

A path in a directed graph is a sequence of directed edges that connects two _________ in a graph.

Two vertices in a graph are adjacent if there is an edge ______ them.

Two vertices in a graph are adjacent if there is an edge connecting them.

An undirected tree is a connected, ______, undirected graph with one element designated as the root.

A ________ is a path in which the first and last vertices are the same and none of the edges are repeated.

A directed graph, sometimes referred as a digraph, is a graph where the edges are _________ pairs of vertices.

An undirected graph is considered complete if it has the maximum number of edges connecting vertices.

An undirected graph is considered complete if it has the maximum number of edges connecting vertices.

A ______ is a sequence of edges that connects two vertices in a graph.

A ______, or a weighted graph, is a graph with weights or costs associated with each edge.

A cycle is a path in which the first and last vertices are the same and only one of the edges are repeated.

A spanning tree is a tree that includes all of the ______ of a graph and some, but possibly not all, of the ______.

A ______ is a spanning tree where the sum of the weights of the edges is less than or equal to the sum of the weights for any other spanning tree for the same graph.

What is an undirected graph?

A path is a sequence of edges that connects two vertices in a graph.

An undirected tree is a connected, cyclic, undirected graph with one element designated as the root.

What is a spanning tree? A minimum spanning tree?

A __________ tree is a tree that includes all of the vertices of a graph and some, but possibly not all, of the edges.

An undirected tree is a connected, acyclic, undirected graph with one element designated as the _______.

A spanning tree is a tree that includes all of the edges of a graph and some, but possibly not all, of the vertices.