1
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
$$(3, 2, 1, 1, 1, 0)$$
2
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 _____.
3
GATE CSE 2013
+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
4
GATE CSE 2012
+2
-0.6
Which of the following graphs is isomorphic to
A
B
C
D
GATE CSE Subjects
EXAM MAP
Medical
NEET