### 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
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
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
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
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
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
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
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
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
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