Math graph fill in words

A finite set of points connected by line segments or curves is called​ ____. 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​ ____

A graph, vertices, edges, loop

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

Equivalent

The number of edges that connect to a vertex is called the​ _____ of the vertex

Degree

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 path that passes through each edge of a graph exactly one time is called​ a(n) ______ path

Euler

A circuit that travels through every edge of a graph exactly once is called​ a/an _______ circuit

Euler

A connected graph has at least one Euler​ path, but no Euler​ circuit, if the graph has exactly​ _______ odd vertices

Two

A connected graph has at least one Euler​ circuit, which, by​ definition, is also an Euler​ path, if the graph has​ _______ odd vertices. An Euler circuit can start and end at​ _______ vertex

No, any

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

Hamilton, Hamilton

A graph that has an edge between each pair of its vertices is called​ a/an ________ 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)!

A graph whose edges have numbers attached to them is called​ a/an ______ 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

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 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 graph that is connected and has no circuits is called​ a/an ____________. For such a​ graph, every edge is​ a/an ____________, and if there are n​ vertices, there must be​ ___________ edges

Tree, bridge, n - 1

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/an ____________ tree

Spanning

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

Minimum spanning

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