1
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
2
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
$$\sum\nolimits_{k = 0}^n {{}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_k}}$$
3
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$${G_2}$$
4
GATE CSE 2004
+2
-0.6
What is the number of vertices in an undirected connected graph with $$27$$ edges, $$6$$ vertices of degree $$2$$, $$\,\,$$ $$3$$ vertices of degree 4 and remaining of degree 3?
A
$$10$$
B
$$11$$
C
$$18$$
D
$$19$$
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
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