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 (B)</p> Signup and view all the answers

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

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

What is a characteristic of a simple graph?

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

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

<p>Adjacent (B)</p> Signup and view all the answers

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

<p>Complete graph (A)</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 (B)</p> Signup and view all the answers

What is a characteristic of a multigraph?

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

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

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

What type of graph may contain multiple edges and loops?

<p>Pseudograph (B)</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 (B)</p> Signup and view all the answers

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