Graph Theory


Q31.

The maximum number of edges in a bipartite graph on 12 vertices is _____.
GateOverflow

Q32.

A cycle on n vertices is isomorphic to its complement. The value of n is _____.
GateOverflow

Q33.

Let G be a graph with n vertices and m edges. What is the tightest upper bound on the running time of Depth First Search on G, when G is represented as an adjacency matrix?
GateOverflow

Q34.

The conic section that is obtained when a right circular cone is cut through a plane that is parallel to the side of the cone is called _____
GateOverflow

Q35.

An ordered n-tuple (d_{1}, d_{2} ,... , d_{n}) with d_{1}\geq d_{2} \geq ... \geq d_{n} is called graphic if there exists a simple undirected graph with n vertices having degrees d_{1}, d_{2} ,... , d_{n} respectively. Which of the following 6-tuples is NOT graphic?
GateOverflow

Q36.

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

Q37.

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

Q38.

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

Q39.

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

Q40.

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