1

GATE CSE 2020

MCQ (Single Correct Answer)

+2

-0.67

Let G = (V, E) be a directed, weighted graph with weight function w: E $$ \to $$ R. For some function f: V $$ \to $$ R, for each edge (u, v) $$ \in $$ E, define w'(u, v) as w(u, v) + f(u) - f(v).

Which one of the options completes the following sentence so that it is TRUE?

βThe shortest paths in G under w are shortest paths under wβ too, _______β.

Which one of the options completes the following sentence so that it is TRUE?

βThe shortest paths in G under w are shortest paths under wβ too, _______β.

2

GATE CSE 2018

MCQ (Single Correct Answer)

+2

-0.6

Let $$G$$ be a simple undirected graph. Let $${T_D}$$ be a depth first search tree of $$G.$$ Let $${T_B}$$ be a
breadth first search tree of $$G.$$ Consider the following statements.

$$(I)$$ No edge of $$G$$ is a cross edge with respect to $${T_D}.$$ ($$A$$ cross edge in $$G$$ is between

$$\,\,\,\,\,\,\,\,$$ two nodes neither of which is an ancestor of the other in $${T_D}.$$)

$$(II)$$ For every edge $$(u,v)$$ of $$G,$$ if $$u$$ is at depth $$i$$ and $$v$$ is at depth $$j$$ in $${T_B}$$, then

$$\,\,\,\,\,\,\,\,\,\,\,$$ $$\left| {i - j} \right| = 1.$$

Which of the statements above must necessarily be true?

3

GATE CSE 2018

Numerical

+2

-0

Let $$G$$ be a graph with $$100!$$ vertices, with each vertex labelled by a distinct permutation of the numbers $$1,2, β¦ , 100.$$ There is an edge between vertices $$u$$ and $$v$$ if and only if the label of $$u$$ can be obtained by swapping two adjacent numbers in the label of $$v.$$ Let $$π¦$$ denote the degree of a vertex in $$G,$$ and $$π§$$ denote the number of connected components in $$G.$$ Then, $$π¦ + 10π§ =$$ _____.

Your input ____

4

GATE CSE 2016 Set 2

MCQ (Single Correct Answer)

+2

-0.6

In an adjacency list representation of an undirected simple graph $$G = (V,E),$$ each edge $$(u, v)$$ has two adjacency list entries: $$[v]$$ in the adjacency list of $$u,$$ and $$[u]$$ in the adjacency list of $$v.$$ These are called twins of each other. A twin pointer is a pointer from an adjacency list entry to its twin. If $$|E| = m$$ and $$|V| = n,$$ and the memory size is not a constraint, what is the time complexity of the most efficient algorithm to set the twin pointer in each entry in each adjacency list?

Questions Asked from Graphs (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE Subjects

Discrete Mathematics

Programming Languages

Theory of Computation

Operating Systems

Computer Organization

Database Management System

Data Structures

Computer Networks

Algorithms

Compiler Design

Software Engineering

Web Technologies

General Aptitude