1
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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 2
Numerical
+2
-0
A cycle on $$n$$ vertices is isomorphic to its complement. The value of $$n$$ is __________.
Your input ____
4
GATE CSE 2013
MCQ (Single Correct Answer)
+2
-0.6
The line graph $$L(G)$$ of a simple graph $$G$$ is defined as follows:

$$\,\,\,\,$$There is exactly one vertex $$v(e)$$ in $$L$$(G)$$ for each edge $$e$$ in $$G$$

$$\,\,\,\,$$ For any two edges $$e$$ and $$e'$$ in $$G$$, $$L(G)$$ has an edge between $$v(e)$$ and $$v(e')$$, if and only if $$e$$ and $$e'$$

$$\,\,\,\,$$ Which of the following statements is/are TRUE?

(P) The line graph of a cycle is a cycle.
(Q) The line graph of a clique is a clique.
(R) The line graph of a planar graph is planar.
(S) The line graph of a tree is a tree.

A
P only
B
P and R only
C
R only
D
P, Q and S only
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