1
GATE CSE 2014 Set 3
+2
-0.6
Let $$\delta$$ denote the minimum degree of a vertex in a graph. For all planar graphs on $$n$$ vertices with $$\delta \ge 3$$, which one of the following is TRUE?
A
In any planar embedding, the number of faces is at least $${n \over 2} + 2$$
B
In any planar embedding, the number of faces is less than $${n \over 2} + 2$$
C
There is a planar embedding in which the number of facess is less than $${n \over 2} + 2$$
D
There is a planar embedding in which the number of faces is at most $${n \over {\delta + 1}}$$
2
GATE CSE 2014 Set 3
+2
-0.6
If $$G$$ is a forest with $$n$$ vertices and $$k$$ connected components, how many edges does $$G$$ have?
A
$$\left\lfloor {n/k} \right\rfloor$$
B
$$\left\lceil {n/k} \right\rceil \,$$
C
$$n - k$$
D
$$n - k + 1$$
3
GATE CSE 2014 Set 1
+2
-0.6
An ordered $$n$$-tuple $$\left( {{d_1},\,\,{d_2},\,....,{d_n}} \right)$$ with $${{d_1} \ge ,\,\,{d_2} \ge .... \ge {d_n}}$$ 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?
A
$$(1, 1, 1, 1, 1, 1)$$
B
$$(2, 2, 2, 2, 2, 2)$$
C
$$(3, 3, 3, 1, 0, 0)$$
D
$$(3, 2, 1, 1, 1, 0)$$
4
GATE CSE 2014 Set 1
Numerical
+2
-0
Consider an undirectional graph $$G$$ where self-loops are not allowed. The vertex set of $$G$$ is $$\left\{ {\left( {i,j} \right):\,1 \le i \le 12,\,1 \le j \le 12} \right\}.$$ There is an edge between $$(a,b)$$ and $$(c,d)$$ if $$\left| {a - c} \right| \le 1$$ and $$\left| {b - d} \right| \le 1$$. The number of edges in this graph is _____.
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
EXAM MAP
Joint Entrance Examination