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.