Multigraphs in Graph Theory

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Questions and Answers

What is a multigraph?

  • A graph with no edges between vertices
  • A graph where all vertices have the same degree
  • A graph where each vertex has a unique edge connected to every other vertex
  • A graph with parallel edges between vertices (correct)

In the context of graphs, what is the degree sequence?

  • The arrangement of vertex degrees in ascending or descending order (correct)
  • The number of vertices in the graph
  • The number of edges in the graph
  • The arrangement of vertices in alphabetical order

What is the complement of a graph?

  • A graph where every edge is replaced by a non-edge (correct)
  • A graph where every vertex is connected to every other vertex
  • A graph with no edges
  • A graph with parallel edges connecting each pair of vertices

What is a star graph?

<p>A graph where one central vertex is connected to all other vertices (C)</p> Signup and view all the answers

In a complete graph, what is true about the number of edges?

<p>The number of edges is equal to the number of vertices (B)</p> Signup and view all the answers

What defines a simple graph?

<p>A graph without any loops or parallel edges (C)</p> Signup and view all the answers

What is a cut vertex in a graph?

<p>A vertex that, when removed, disconnects the graph (C)</p> Signup and view all the answers

How is a cut edge defined in a graph?

<p>An edge that, when removed, results in a disconnected graph (A)</p> Signup and view all the answers

What is the maximum number of cut edges possible in a connected graph with 'n' vertices?

<p>$n-1$ (B)</p> Signup and view all the answers

If a cut vertex exists in a graph, what can be inferred about the existence of a cut edge?

<p>The existence of a cut edge is independent of the cut vertex (C)</p> Signup and view all the answers

What defines a cut set of a graph?

<p>A subset of edges that disconnects the graph when removed (D)</p> Signup and view all the answers

What happens to a graph when a cut edge is removed?

<p>The number of components in the graph increases (A)</p> Signup and view all the answers

What is a star graph?

<p>A graph with only one vertex connected to all other vertices. (B)</p> Signup and view all the answers

What is the complement of a graph?

<p>A graph consisting of isolated vertices. (D)</p> Signup and view all the answers

What is a simple graph?

<p>A graph that has no loops or multiple edges between the same pair of vertices. (E)</p> Signup and view all the answers

What is a complete graph?

<p>A graph where every vertex is connected to every other vertex. (E)</p> Signup and view all the answers

Which of the following statements about edges in a graph is true?

<p>Edges are used to represent the relationships between pairs of vertices. (A)</p> Signup and view all the answers

In which type of graph are all possible edges present between distinct vertices?

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

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