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Topological Graph Theory

This quiz covers the fundamental concepts and theorems of Topological Graph Theory, a branch of mathematics that studies graphs from a topological perspective.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

In graph theory, a path is a sequence of vertices such that consecutive vertices are connected by edges. What is the maximum number of edges in a path with n vertices?

  1. n-1
  2. n
  3. n+1
  4. 2n
Question 2 Multiple Choice (Single Answer)

A cycle in a graph is a path that begins and ends at the same vertex. What is the minimum number of edges in a cycle with n vertices?

  1. n
  2. n+1
  3. 2n
  4. 3n
Question 3 Multiple Choice (Single Answer)

A graph is called connected if there is a path between every pair of vertices. What is the maximum number of edges that can be removed from a connected graph with n vertices so that it remains connected?

  1. n-1
  2. n
  3. n+1
  4. 2n-1
Question 4 Multiple Choice (Single Answer)

A tree is a connected graph with no cycles. What is the maximum number of edges that a tree with n vertices can have?

  1. n-1
  2. n
  3. n+1
  4. 2n-1
Question 5 Multiple Choice (Single Answer)

A graph is called Eulerian if it contains a cycle that visits every edge exactly once. What is a necessary and sufficient condition for a graph to be Eulerian?

  1. Every vertex has even degree
  2. Every vertex has odd degree
  3. The graph is connected
  4. The graph has no cycles
Question 6 Multiple Choice (Single Answer)

A graph is called Hamiltonian if it contains a cycle that visits every vertex exactly once. What is a sufficient condition for a graph to be Hamiltonian?

  1. The graph is complete
  2. The graph is connected
  3. The graph has no cycles
  4. The graph is Eulerian
Question 7 Multiple Choice (Single Answer)

The girth of a graph is the length of the shortest cycle in the graph. What is the girth of a tree?

  1. 1
  2. 2
  3. 3
  4. Infinity
Question 8 Multiple Choice (Single Answer)

The chromatic number of a graph is the minimum number of colors needed to color the vertices of the graph so that no two adjacent vertices have the same color. What is the chromatic number of a complete graph with n vertices?

  1. 1
  2. n
  3. n+1
  4. 2n
Question 9 Multiple Choice (Single Answer)

The independence number of a graph is the maximum number of vertices that can be selected such that no two selected vertices are adjacent. What is the independence number of a complete graph with n vertices?

  1. 1
  2. n
  3. n-1
  4. 0
Question 10 Multiple Choice (Single Answer)

The clique number of a graph is the maximum number of vertices that can be selected such that every pair of selected vertices is adjacent. What is the clique number of a complete graph with n vertices?

  1. 1
  2. n
  3. n-1
  4. n+1
Question 11 Multiple Choice (Single Answer)

The domination number of a graph is the minimum number of vertices that need to be selected such that every other vertex is adjacent to at least one selected vertex. What is the domination number of a complete graph with n vertices?

  1. 1
  2. n
  3. n-1
  4. n+1
Question 12 Multiple Choice (Single Answer)

The matching number of a graph is the maximum number of edges that can be selected such that no two selected edges share a common vertex. What is the matching number of a complete graph with n vertices?

  1. n
  2. n-1
  3. n/2
  4. n+1
Question 13 Multiple Choice (Single Answer)

The vertex cover number of a graph is the minimum number of vertices that need to be selected such that every edge of the graph is incident to at least one selected vertex. What is the vertex cover number of a complete graph with n vertices?

  1. n
  2. n-1
  3. n/2
  4. n+1
Question 14 Multiple Choice (Single Answer)

The edge cover number of a graph is the minimum number of edges that need to be selected such that every vertex of the graph is incident to at least one selected edge. What is the edge cover number of a complete graph with n vertices?

  1. n
  2. n-1
  3. n/2
  4. n+1
Question 15 Multiple Choice (Single Answer)

The arboricity of a graph is the minimum number of forests into which the edges of the graph can be partitioned. What is the arboricity of a complete graph with n vertices?

  1. 1
  2. n
  3. n-1
  4. n+1
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