Multiple Choice Questions On Discrete Structure - Set 3

1) A tour of G is a closed walk of graph G which includes every edge G at least once. A ..... tour of G is a tour which includes every edge of G exactly once ?
  1. Hamiltonian
  2. Planar
  3. Isomorphic
  4. Euler
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Answer = D 
Explanation: If some closed walk in a graph contains all the edges then the walk is called Euler.
2) Which of the following is not a type of graph ?
  1. Euler
  2. Hamiltonian
  3. Tree
  4. Path
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Answer = D 
Explanation:Path is a way from one node no another but not a graph.

3) Choose the most appropriate definition of plane graph ?
  1. A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices
  2. A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non - empty disjoint subset X and Y in such a way that each edge of G has one end in X and one end in Y.
  3. A simple graph which is Isomorphic to Hamiltonian graph
  4. None of these
Show/Hide Answer
Answer = A
Explanation: No explanation for this question.
4) A continuous non - intersecting curve in the plane whose origin and terminus coincide ?
  1. Planer
  2. Jordan
  3. Hamiltonian
  4. All of these
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Answer = B 
Explanation: The jordan graph is the set of all vertices of minimum eccentricity that is the set of all vertices A where the greatest distance to other vertex B is minimal.
5) Polyhedral is.... ?
  1. A simple connected graph
  2. A plane graph
  3. A graph in which the degree of every vertex and every face is atleast 3
  4. All of above
Show/Hide Answer
Answer = D 
Explanation: A polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron

6) A path in graph G, which contains every vertex of G once and only once ?
  1. Eulartour
  2. Hamiltonian Path
  3. Eular trail
  4. Hamiltonian tour
Show/Hide Answer
Answer = B 
Explanation:A Hamiltonian circuit in a connected graph is defined as a closed walk that traverse every vertex of G exactly once except the starting vertex.

7) A minimal spanning tree of a graph G is.... ?
  1. A spanning sub graph
  2. A tree
  3. Minimum weights
  4. All of above
Show/Hide Answer
Answer = D 
Explanation: A tree is said to be spanning tree of connected graph G if it is subgraph of G and contains all the vertices of G.
8) A tree having a main node, which has no predecessor is.... ?
  1. Spanning tree
  2. Rooted tree
  3. Weighted tree
  4. None of these
Show/Hide Answer
Answer = B 
Explanation:A tree in which one vertex distinguish from all other is called rooted tree.

9) Diameter of a graph is denoted by diam(G) is defined by.... ?
  1. max (e(v) : v belongs to V)
  2. max( d(u,v) )
  3. Both A and B
  4. None of these
Show/Hide Answer
Answer = C 
Explanation: The diameter of a graph G is largest distance between two vertices in a graph G.
 
10) A vertex of a graph is called even or odd depending upon ?
  1. Total number of edges in a graph is even or odd
  2. Total number of vertices in a graph is even or odd
  3. Its degree is even or odd
  4. None of these
Show/Hide Answer
Answer = C
Explanation: The vertex of a graph is called even or odd based on its degree.


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