1
GATE CSE 2012
+2
-0.6
Which of the following graphs is isomorphic to
A
B
C
D
2
GATE CSE 2012
+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
$$360$$
3
GATE CSE 2010
+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 $${\rm I}$$$$V$$
4
GATE CSE 2008
+2
-0.6
Which of the following statements is true for every planar graph on $$n$$ vertices?
A
The graph is connected
B
The graph is Eulerian
C
The graph has a vertex-cover of size at most $$3n/4$$
D
The graph has an independent set of size at least $$n/3$$
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