chapter1:1.4

Multiple Choice

Which of the following best describes the significance of understanding the language of graphs in mathematics?

• It helps in interpreting data visually and making informed decisions.

• It is only useful for drawing pictures.

• It is not relevant to real-world problems.

• It is mainly used for artistic purposes.

Multiple Choice

Based on the information provided in the table and diagram, which group of three people would form a team where everyone has previously worked together?

• Bev, Cai, Flo

• Ana, Dan, Ed

• Hal, Gia, Ira

• Ed, Dan, Hal

Multiple Select

Which of the following are possible features of a graph as shown in the diagram?

• Parallel edges

• Loops

• Isolated vertices

• Vertices with no edges

Multiple Choice

Which of the following statements about the structure of a graph is correct?

• Vertices are the dots and edges are the lines connecting them.

• Edges are the dots and vertices are the lines connecting them.

• Graphs always represent equations.

• Vertices can never be connected to themselves.

Multiple Choice

Which of the following best describes a loop in a graph?

• An edge connecting two different vertices

• An edge connecting a vertex to itself

• Two edges connecting the same pair of vertices

• A vertex with no incident edges

Multiple Choice

Based on the formal definition, what does it mean for two edges to be parallel in a graph?

• They connect the same pair of endpoints

• They are incident on the same vertex

• They form a loop

• They are adjacent to each other

Multiple Select

Which of the following are true about the graph shown in Example 1.4.1?

• v4 is an isolated vertex

• e2 and e3 are parallel edges

• e6 and e7 are loops

• v1 is adjacent to v4

Multiple Choice

Which edges in Example 1.4.2 are incident to vertex v4?

• e2 and e3

• e1 and e4

• e1 and e2

• e3 and e4

Multiple Choice

Which of the following is the correct vertex set for the graph described in Example 1.4.2?

• {v1, v2, v3, v4}

• {v1, v2, v3, v4, v5}

• {e1, e2, e3, e4}

• {v1, v2, v3}

Multiple Choice

Which of the following is the correct edge-endpoint function for the graph in Figure 1.4.1(b)?

• e1: {v1, v2}, e2: {v2, v3}, e3: {v3, v4}, e4: {v4, v5}, e5: {v5, v1}

• e1: {v1, v3}, e2: {v2, v4}, e3: {v2, v4}, e4: {v3}, e5: {v1, v2}

• e1: {v1, v2}, e2: {v2, v4}, e3: {v3, v5}, e4: {v4, v1}, e5: {v5, v3}

• e1: {v1, v2}, e2: {v2, v3}, e3: {v3, v1}, e4: {v4, v5}, e5: {v5, v4}

Multiple Choice

Which of the following systems can be represented by graphs?

• Telephone systems

• Electric power systems

• Gas pipeline systems

• All of the above

Open Ended

Explain how the hub-and-spoke model is used to represent a network in graph theory.

Multiple Select

Select all properties that are true for a directed graph (digraph).

• Edges are associated with ordered pairs of vertices.

• Each edge has endpoints.

• Edges are always bidirectional.

• A directed edge goes from one vertex to another.

Multiple Choice

Which of the following statements is true about directed graphs?

• Each edge is associated with an unordered pair of vertices.

• Each edge is associated with an ordered pair of vertices.

• Directed graphs cannot have endpoints.

• Directed graphs are the same as undirected graphs.

Open Ended

How can graphs be used in artificial intelligence to represent and infer knowledge?

Open Ended

What questions do you still have about speaking mathematically or using the language of graphs?

Open Ended

How has your understanding of the language of graphs improved after this lesson?