Discrete Mathematics


Q81.

Consider an undirected graph G where self-loops are not allowed. The vertex set of G is {(i,f):1\leqi\leq12, 1\leqj\leq12}. There is an edge between (a,b) and (c,d) if |a-c|\leq1 and |b-d| \leq1. The number of edges in the graph is ____.
GateOverflow

Q82.

Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G ?
GateOverflow

Q83.

Consider the directed graph given below. Which one of the following is TRUE?
GateOverflow

Q84.

How many diagonals can be drawn by joining the angular points of an octagon?
GateOverflow

Q85.

The number of edges in a 'n' vertex complete graph is?
GateOverflow

Q86.

Suppose depth first search is executed on the graph below starting at some unknown vertex. Assume that a recursive call to visit a vertex is made only after first checking that the vertex has not been visited earlier. Then the maximum possible recursion depth (including the initial call) is _________.
GateOverflow

Q87.

What is the cyclomatic complexity of a module which has seventeen edges and thirteen nodes?
GateOverflow

Q88.

Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even.
GateOverflow

Q89.

Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?
GateOverflow

Q90.

Let G be a group of order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?
GateOverflow