1
GATE CSE 2005
+2
-0.6
Which one of the following graphs is NOT planar?
A
G1
B
G2
C
G3
D
G4
2
GATE CSE 2004
+2
-0.6
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same colour, is
A
2
B
3
C
4
D
5
3
GATE CSE 2004
+2
-0.6
How many graphs on $$n$$ labeled vertices exist which have at least $$\left( {{n^2} - 3n} \right)/2\,\,\,$$ edges?
A
$${}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_{\left( {{n^ \wedge }2 - 3n} \right)/2}}$$
B
$${\sum\limits_{k = 0}^{\left( {{n^ \wedge }2 - 3n} \right)/2} {{}^{\left( {{n^ \wedge }2 - n} \right)}{C_k}} }$$
C
$${}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_n}$$
D
$$\sum\nolimits_{k = 0}^n {{}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_k}}$$
4
GATE CSE 2004
+2
-0.6
Let $${G_1} = \left( {V,\,{E_1}} \right)$$ and $${G_2} = \left( {V,\,{E_2}} \right)$$ be connected graphs on the same vertex set $$V$$ with more than two vertices. If $${G_1} \cap {G_2} = \left( {V,{E_1} \cap {E_2}} \right)$$ is not a connected graph, then the graph $${G_1} \cup {G_2} = \left( {V,{E_1} \cup {E_2}} \right)$$
A
cannot have a cut vertex
B
must have a cycle
C
must have a cut-edge (bridge)
D
has chromatic number strictly greater than those of $${G_1}$$ and$${G_2}$$
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