1
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+2
-0.67
Let G be a group order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?
A
G is always cyclic, but H may not be cyclic.
B
G may not be cyclic, but H is always cyclic.
C
Both G and H are always cyclic.
D
Both G and H may not be cyclic.
2
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+2
-0.67

Let G = (V, E) be an undirected unweighted connected graph. The diameter of G is defined as:

diam(G) = $$\displaystyle\max_{u, x\in V}$$ {the length of shortest path between u and v}

Let M be the adjacency matrix of G.

Define graph G2 on the same set of vertices with adjacency matrix N, where

$$N_{ij} =\left\{ {\begin{array}{*{20}{c}} {1 \ \ \text{if} \ \ {M_{ij}} > 0 \ \ \text{or} \ \ P_{ij} > 0, \ \text{where} \ \ P = {M^2}}\\ {0, \ \ \ \ \ \text{otherwise}} \end{array}} \right.$$

Which one of the following statements is true?

A
diam(G) < diam(G2) ≤ diam(G)
B
$$\left\lceil {diam(G)/2} \right\rceil $$ < diam(G2) < diam(G)
C
diam(G2) ≤ $$\left\lceil {diam(G)/2} \right\rceil $$
D
diam(G2) = diam(G)
3
GATE CSE 2020
Numerical
+2
-0
Graph G is obtained by adding vertex s to K3,4 and making s adjacent to every vertex of K3,4. The minimum number of colours required to edge-colour G is _____.
Your input ____
4
GATE CSE 2019
MCQ (Single Correct Answer)
+2
-0.67

Let G be any connected, weighted, undirected graph.

I. G has a unique minimum spanning tree, if no two edges of G have the same weight.

II. G has a unique minimum spanning tree, if, for every cut of G, there is a unique minimum-weight edge crossing the cut.

Which of the above two statements is/are TRUE?

A

I only

B

II only

C

Both I and II

D

Neither I nor II

GATE CSE Subjects
Software Engineering
Web Technologies
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12