1
GATE CSE 2018
Numerical
+1
-0
Let $$G$$ be a finite group on $$84$$ elements. The size of a largest possible proper subgroup of $$G$$ is ________.
2
GATE CSE 2018
Numerical
+1
-0
The chromatic number of the following graph is _______.
3
GATE CSE 2016 Set 2
Numerical
+1
-0
The minimum number of colours that is sufficient to vertex-colour any planar graph is _____________ .
4
GATE CSE 2014 Set 1
+1
-0.3
Let $$G = \left( {V,E} \right)$$ 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 $$G$$?
A
$${G_1} = \left( {V,\,\,{E_1}} \right)\,\,\,$$where $$\,\,{E_1} = \left\{ {\left( {u,v} \right) \notin E} \right\}$$
B
$${G_2} = \left( {V,\,\,{E_2}} \right)\,\,\,$$ where $$\,\,\,{E_2} = \left\{ {\left( {u,v} \right) \in E} \right\}$$
C
$${G_3} = \left( {V,\,\,{E_3}} \right)\,\,\,$$ where $$\,\,{E_3} =$$ {$${\left( {u,v} \right)\left| \, \right.}$$ there isa path of length $$\le 2$$ from $$u$$ to $$v$$ in $$E$$}
D
$${G_4} = \left( {{V_4},\,\,{E_{}}} \right)\,\,\,$$ where $${{V_4}}$$ is the set of vertices in $$G$$ which are not isolated.
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