Required informationSkip to questionNOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.What kind of graph from the following table can be used to model a highway system between major cities, where  there is an edge between the vertices representing cities for each interstate highway between them and there is a loop at the vertex representing a city if there is an interstate highway that circles this city?Multiple ChoicePseudographMultigraphSimple graphMixed graph

Based on the given information, we are looking for a type of graph that can model a highway system between major cities. The graph should have edges representing interstate highways between cities and loops at vertices representing cities with interstate highways that circle them.

Let's analyze the options:

1. Pseudograph: A pseudograph is a graph that allows multiple edges between the same pair of vertices and loops at vertices. This option fits the requirement of having loops at vertices representing cities with interstate highways that circle them. However, it does not specify whether there is an edge between vertices representing cities for each interstate highway between them. Therefore, a pseudograph may not be the best choice for modeling a highway system between major cities.

2. Multigraph: A multigraph is a graph that allows multiple edges between the same pair of vertices but does not allow loops at vertices. Similar to a pseudograph, a multigraph does not explicitly state whether there is an edge between vertices representing cities for each interstate highway between them. Therefore, a multigraph may not be the most suitable choice for modeling a highway system between major cities.

3. Simple graph: A simple graph is a graph that does not allow multiple edges between the same pair of vertices or loops at vertices. This option does not meet the requirement of having loops at vertices representing cities with interstate highways that circle them. Therefore, a simple graph is not the correct choice for modeling a highway system between major cities.

4. Mixed graph: A mixed graph is a graph that allows both directed and undirected edges. This option does not specify whether the graph allows multiple edges between the same pair of vertices or loops at vertices. Therefore, a mixed graph may not be the most appropriate choice for modeling a highway system between major cities.

Based on the given requirements, the most suitable type of graph to model a highway system between major cities, where there is an edge between the vertices representing cities for each interstate highway between them and there is a loop at the vertex representing a city if there is an interstate highway that circles this city, would be a pseudograph.