State the number of vertices and edges for the following networks:
State whether the following networks are non-valid:
Is the number of edges greater than the number of vertices in the given network?
For each of the given networks, list the pairs of vertices that have an edge between them:
Consider the given graph:
State the number of edges connected to vertex A.
List the vertices adjacent to vertex E.
Name the vertex that is directly connected to all other vertices.
Name the vertex that is not directly connected to vertex A.
State whether the following networks demonstrate the statement "One pair of vertices has more than one edge between them":
State whether the following statements are true or false in relation to all networks:
There is always at least one vertex.
There is always at least one edge.
All vertices must be connected to every other vertex by edges.
An edge can start and end at the same vertex.
Edges always start and end at vertices.
An edge can connect three vertices together.
State whether the following networks are directed or undirected:
Determine whether the following situations would be best represented by a directed or undirected network:
The countries that border each other
The results of an elimination-style sports tournament
The animal food chain
Your parents and their ancestors
Ways to get from one classroom to another at school
How parts of the body are connected
Consider the following networks:
State the weight of the edge from S to Q.
Calculate the weight of the entire network.
State the weight of the edge connecting Q and S.
Calculate the weight of the entire network.
Consider the graph:
State the number of arcs that begin at vertex Z.
State the weight of the arc BC.
Consider the graph:
State the number of arcs that end at vertex T.
Calculate the total weight of all arcs that end at vertex V.
Define the following in terms of graph theory:
A loop
How many loops are in the following networks:
For each of the given networks, state which of the highlighted edges are bridges:
What degree does a loop have?
Consider the following networks:
State the degree of vertex C.
State the degree of vertex D.
State the degree of vertex X.
State the degree of vertex C.