1
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
2
GATE CSE 2012
MCQ (Single Correct Answer)
+2
-0.6
Which of the following graphs is isomorphic to GATE CSE 2012 Discrete Mathematics - Graph Theory Question 62 English
A
GATE CSE 2012 Discrete Mathematics - Graph Theory Question 62 English Option 1
B
GATE CSE 2012 Discrete Mathematics - Graph Theory Question 62 English Option 2
C
GATE CSE 2012 Discrete Mathematics - Graph Theory Question 62 English Option 3
D
GATE CSE 2012 Discrete Mathematics - Graph Theory Question 62 English Option 4
3
GATE CSE 2012
MCQ (Single Correct Answer)
+2
-0.6
Let $$G$$ be a complete undirected graph on $$6$$ vertices. If vertices of $$G$$ $$\,\,\,\,$$ are labeled, then the number of distinct cycles of length $$4$$ in $$G$$ is equal to
A
$$15$$
B
$$30$$
C
$$90$$
D
$$360$$
4
GATE CSE 2010
MCQ (Single Correct Answer)
+2
-0.6
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
$${\rm I}.$$$$\,\,\,\,\,7,6,5,4,4,3,2,1$$
$${\rm I}{\rm I}.$$$$\,\,\,\,\,6,6,6,6,3,3,2,2$$
$${\rm I}{\rm I}{\rm I}.$$$$\,\,\,\,\,7,6,6,4,4,3,2,2$$
$${\rm I}V.$$$$\,\,\,\,\,8,7,7,6,4,2,1,1$$
A
$${\rm I}$$ and $${\rm I}$$$${\rm I}$$
B
$${\rm I}$$$${\rm I}$$$${\rm I}$$ and $${\rm I}$$$$V$$
C
$${\rm I}$$$$V$$ only
D
$${\rm I}$$$${\rm I}$$ and $${\rm I}$$$$V$$
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