Graph Theory
This quiz covers fundamental concepts and properties of graph theory, a branch of mathematics that studies the relationships between vertices and edges in graphs.
Questions
What is the maximum number of edges in a simple graph with n vertices?
- n(n-1)
- n(n+1)
- n^2
- 2n
Which of the following graphs is acyclic?
- Tree
- Cycle
- Complete graph
- Star graph
What is the degree of a vertex in a graph?
- Number of edges incident to the vertex
- Number of vertices adjacent to the vertex
- Number of paths starting from the vertex
- Number of cycles containing the vertex
Which of the following is a property of a bipartite graph?
- It can be partitioned into two disjoint sets of vertices
- It contains an odd cycle
- It is always connected
- It has an Eulerian path
What is the minimum number of colors required to color the vertices of a graph such that no two adjacent vertices have the same color?
- Chromatic number
- Degree of the graph
- Number of vertices in the graph
- Number of edges in the graph
Which of the following is a necessary condition for a graph to be Hamiltonian?
- It must be connected
- It must be complete
- It must have an Eulerian path
- It must have an odd number of vertices
What is the maximum number of edges in a spanning tree of a connected graph with n vertices?
- n-1
- n
- n+1
- 2n-1
Which of the following is a sufficient condition for a graph to be planar?
- It must have an Eulerian path
- It must be acyclic
- It must have a vertex of degree at most 3
- It must be bipartite
What is the maximum number of edges in a complete bipartite graph with m vertices in one part and n vertices in the other part?
- mn
- m(n-1)
- n(m-1)
- m+n
Which of the following is a necessary condition for a graph to be Eulerian?
- It must be connected
- It must be acyclic
- It must have an even number of vertices
- It must have an odd number of vertices
What is the maximum number of edges in a simple graph with n vertices and m edges?
- n(n-1)/2
- n(n+1)/2
- m(m+1)/2
- m(m-1)/2
Which of the following is a necessary condition for a graph to be Hamiltonian?
- It must be connected
- It must be complete
- It must have an Eulerian path
- It must have an odd number of vertices
What is the maximum number of edges in a spanning tree of a connected graph with n vertices?
- n-1
- n
- n+1
- 2n-1
Which of the following is a sufficient condition for a graph to be planar?
- It must have an Eulerian path
- It must be acyclic
- It must have a vertex of degree at most 3
- It must be bipartite
What is the maximum number of edges in a complete bipartite graph with m vertices in one part and n vertices in the other part?
- mn
- m(n-1)
- n(m-1)
- m+n