Math Ch. 13

Loop

An edge that connects a vertex to itself.

Minimum-cost

The least expensive spanning tree of all spanning trees under consideration is called the _____________ spanning tree.

Kruskal's

To determine the minimum-cost spanning tree for a weighted graph, we can use _____________ algorithm.

Disconnected

A bridge is an edge that, if removed from a connected graph would create a ______________ graph.

Tree

A connected graph in which each edge is a bridge

Edge

A line segment in a graph

B

If a connected graph has exactly two odd vertices, A and B, then each Euler path must begin at vertex A and end at vertex _______, or begin at vertex B and end at Vertex A.

Optimal

In a traveling salesman problem, the Hamilton circuit with the lowest associated cost or shortest distance is called the ______________ solution

Traveling Salesman problems

Problems that generally involve seeking the least expensive or shortest way to travel among several locations are called

Euler circuit

A circuit that passes through each edge of a graph exactly one time is.

No

A connected graph has at least one Euler path that is also an Euler circuit, if the graph has ___ odd vertices.

Two

A connected graph has at least one Euler path, but no Euler circuits, if the graph has exactly ____ odd vertices.

Odd

A connected graph has neither an Euler path nor an Euler circuit, if the graph has more than two _____ vertices.

Graph

A finite set of points connected by line segments.

Complete graph

A graph that has exactly one edge between each pair of vertices

Weighted

A graph that has numbers along the edges to indicate cost or distance is called a __________ graph

Hamilton circuit

A path that begins and ends at the same vertex and passes through all other vertices of a graph exactly one time

Circuit

A path that begins and ends with the same vertex.

Euler path

A path that passes through each edge of a graph exactly one time.

Vertex

A point in a graph

Path

A sequence of adjacent vertices and the edges connecting them.

Circuits

A tree does not have any Euler or Hamilton _________.

Spanning tree

A tree that is created from another graph by removing edges while still maintaining a path to each vertex is called a _________.

If you remove any edge in a tree, it creates a...

Disconnected graph

Euler

Every complete graph has a Hamilton circuit but not necessarily an ___________ circuit.

Brute force method

The method discussed in this section that will determine the optimal solution to a traveling salesmen problem

Nearest neighbor method

The methods discussed in this section that will determine an approximate solution to a traveling salesman problem is the

Degree

The number of edges that connect to a vertex is called the __________ of a vertex.