math 1029 ledet exam 3 vocab

A procedure that yields the minimum spanning tree of a graph is called _____________ Algorithm. The idea of the algorithm is to always pick the edge with the smallest available _________, but avoid creating any ___________.

Kruskal's weight circuits

A method that determines the solution to the traveling salesperson problem involves listing all Hamilton circuits and selecting the circuit with the minimum sum of weights. This method is called the _______________ method.

Brute Force

A path that passes through each vertex of a graph exactly once is called a ______________ path. Such a path that begins and ends at the same vertex and passes through all other vertices exactly once is called a _____________ circuit.

Hamilton Hamilton

True/False: An edge can be a part of a path only once.

True because a path is a sequence of adjacent vertices and the edges connecting them.

If there is at least one edge connecting two vertices in a graph, the vertices are called ____________. A sequence of such vertices and the edges connecting them is called a ___________. If this sequence of vertices and connecting edges begins and ends at the same vertex, it is called a _____________.

adjacent path circuit

A graph that has an edge between each pair of its vertices is a __________ graph. If such a graph has "n" vertices, the number of Hamilton circuits in the graph is given by the factorial expression ____________.

complete (n-1)!

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

degree

Two graphs that have the same number of vertices connected to each other in the same way are called _______________.

equivalent

A finite set of points connected by line segments or curves is called a ____________. The points are called ____________. The line segments or curves are called ___________. Such a line segment or curve that starts and ends at the same point is called a __________.

graph vertices edges loop

A tree that is created from a weighted graph and that has the smallest possible weight is called the __________________ tree.

minimum spanning

A method that approximates the solution to the salesperson problem is called the _____________ method. This method involves continually choosing an edge with the smallest __________.

nearest neighbor weight

A tree that is created from another connected graph and that contains all of the connected graph's vertices, is connected, and contains no circuits is called a ____________ tree.

spanning

A graph that is connected and has no circuits is called a _________. For such a graph, every edge is a ___________, and if there are "n" vertices, there must be _________ edges.

tree bridge n-1

A graph whose edges have numbers attached to them is called a __________ graph. The numbers shown along the edges of such a graph are called the ________ of the edges. The problem of finding a Hamilton circuit for which the sum of these numbers is a minimum is called the _____________ salesperson problem. Such a Hamilton circuit is called the ________ solution.

weighted weights traveling optimal