Discrete Mathematics


Q61.

Breadth First Search(BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is______ .
GateOverflow

Q62.

The maximum number of edges in a n-node undirected graph without self loops is
GateOverflow

Q63.

In a connected graph, a bridge is an edge whose removal disconnects a graph. Which one of the following statements is true?
GateOverflow

Q64.

The Breadth First Search (BFS) algorithm has been implemented using the queue data structure. Which one of the following is a possible order of visiting the nodes in the graph below?
GateOverflow

Q65.

Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is ___________.
GateOverflow

Q66.

G is undirected graph with n vertices and 25 edges such that each vertex of G has degree at least 3. Then the maximum possible value of n is ___________.
GateOverflow

Q67.

The minimum number of colours that is sufficient to vertex-colour any planar graph is _________.
GateOverflow

Q68.

The chromatic number of the following graph is _______.
GateOverflow

Q69.

A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on n vertices, n is
GateOverflow

Q70.

Consider the following directed graph: The number of different topological orderings of the vertices of the graph is
GateOverflow