Graph Theory: Edge Types and Graph Definitions
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Questions and Answers

What is a set of vertices and a set of undirected edges each of which is associated with a set of one or two of these vertices?

  • An undirected graph (correct)
  • A directed graph
  • A pseudograph
  • A multigraph

    • What is the degree of a vertex v in an undirected graph?

  • The number of vertices adjacent to v
  • The number of edges incident with v with loops counted twice (correct)
  • The number of edges incident with v with loops counted once
  • The number of edges between v and its adjacent vertices

    • What is a graph with directed edges that may contain multiple directed edges?

  • A simple directed graph
  • A pseudograph
  • A directed graph
  • A directed multigraph (correct)

    • What is an edge connecting a vertex with itself?

    <p>A loop</p> Signup and view all the answers

    What is an undirected graph with no multiple edges or loops?

    <p>A simple graph</p> Signup and view all the answers

    What is the underlying undirected graph of a graph with directed edges?

    <p>The graph obtained by ignoring the directions of the edges</p> Signup and view all the answers

    What is the out-degree of the vertex v in a graph with directed edges?

    <p>The number of edges with v as their initial vertex</p> Signup and view all the answers

    What is a graph with vertex set that can be partitioned into subsets V1 and V2 so that each edge connects a vertex in V1 and a vertex in V2?

    <p>A bipartite graph</p> Signup and view all the answers

    What is a graph with vertex set that has an edge between each pair of vertices?

    <p>A complete graph</p> Signup and view all the answers

    What is a characteristic of a simple graph?

    <p>It has no multiple edges or loops</p> Signup and view all the answers

    What is the term for two vertices connected by an edge?

    <p>Adjacent</p> Signup and view all the answers

    What type of graph has an edge between each pair of vertices?

    <p>Complete graph</p> Signup and view all the answers

    What is the in-degree of a vertex v in a graph with directed edges?

    <p>The number of edges with v as their terminal vertex</p> Signup and view all the answers

    What is a characteristic of a multigraph?

    <p>It may contain multiple edges</p> Signup and view all the answers

    What is a characteristic of a directed edge?

    <p>It is associated with an ordered pair of vertices</p> Signup and view all the answers

    What is the term for an edge associated with a set {u, v}?

    <p>Undirected edge</p> Signup and view all the answers

    What type of graph may contain multiple edges and loops?

    <p>Pseudograph</p> Signup and view all the answers

    What is the out-degree of a vertex v in a graph with directed edges?

    <p>The number of edges with v as their initial vertex</p> Signup and view all the answers

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