This practice GATE test includes only graph theory questions, which are part of the GATE question papers for mathematics. Solve GATE previous papers to crack GATE 2012 exam and get admission in IITs.
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Consider a simple connected graph G with n vertices and n edges(n>2). Then which of the following statements are TRUE ?
G has atleast one cycle
G has no cycles
The graph obtained by removing any edge from G is not connected.
G has atleast one cycle and The graph obtained by removing any edge from G is not connected.
The number of distinct simple graphs with up to three nodes is…........
9
7
10
15
Consider the graph G where V(G)={A,B,C,D} and E(G)=[{A,B},{B,C},{C,D}]. The degree of each vertices A,B,C,D respectively in G are…..
1,2,3,2
1,3,2,2
1,1,1,1
1,2,2,3
maximum number of edges in a n-node undirected graph without self loops is….......
let G be a graph with 100 vertices numbered 1 to 100. Two vertices i and j are adjacent if |i-j|=8 or |i-j|=12. The number of connected components in G is…......
8
12
25
4
A graph in which all nodes are of equal degree is known as…....
complete graph
multi graph
non regular graph
regular graph
The minimum number of spanning trees in a connected graph with “n” nodes is…..
n-1
n/2
2
1
The minimum number of edges in a connected cyclic graph on ‘n’ vertices is…....
n
n+1
none of these
The minimum number of colours required to colour the vertices of a cycle with “n” nodes in such a way that no two adjacent nodes have the same colour is….......
n-2[n/2]+2
3
A graph is planar if and only if it does not contain …..
sub graphs isomorpic to or
a sub graph homomorpic to or
sub graphs isomorpic to and
sub graphs homomorpic to and
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