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Syllabus: Connectivity, Matching, Coloring.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&1&0&0&1&1&0&1&0&1&0&0.6&1
\\\hline\textbf{2 Marks Count} & 3 &1&0&1&1&1&0&0&0&0&0&0.7&3
\\\hline\textbf{Total Marks} & 7 &3&0&2&3&3&0&1&0&1&\bf{0}&\bf{2}&\bf{7}\\\hline
\end{array}}}$$

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Recent questions in Graph Theory

29 votes
4 answers
982
GATE CSE 2012 | Question: 26
Which of the following graphs is isomorphic to
Which of the following graphs is isomorphic to
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25 votes
2 answers
984
GATE CSE 2013 | Question: 25
Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. P only Q only Both P and Q Neither P nor Q
Which of the following statements is/are TRUE for undirected graphs?P: Number of odd degree vertices is even.Q: Sum of degrees of all vertices is even. P only Q only Both...
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39 votes
5 answers
986
GATE CSE 1999 | Question: 1.15
The number of articulation points of the following graph is $0$ $1$ $2$ $3$
The number of articulation points of the following graph is$0$$1$$2$$3$
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76 votes
5 answers
987
GATE CSE 2007 | Question: 23
Which of the following graphs has an Eulerian circuit? Any $k$-regular graph where $k$ is an even number. A complete graph on $90$ vertices. The complement of a cycle on $25$ vertices. None of the above
Which of the following graphs has an Eulerian circuit?Any $k$-regular graph where $k$ is an even number.A complete graph on $90$ vertices.The complement of a cycle on $25...
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19 votes
3 answers
988
GATE CSE 2007 | Question: 4
Let $G$ be the non-planar graph with the minimum possible number of edges. Then $G$ has 9 edges and 5 vertices 9 edges and 6 vertices 10 edges and 5 vertices 10 edges and 6 vertices
Let $G$ be the non-planar graph with the minimum possible number of edges. Then $G$ has9 edges and 5 vertices9 edges and 6 vertices10 edges and 5 vertices10 edges and 6 v...
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15 votes
2 answers
989
GATE CSE 2005 | Question: 47
Which one of the following graphs is NOT planar? G1 G2 G3 G4
Which one of the following graphs is NOT planar? G1G2G3G4
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38 votes
4 answers
990
GATE CSE 2005 | Question: 11
Let $G$ be a simple graph with $20$ vertices and $100$ edges. The size of the minimum vertex cover of G is $8$. Then, the size of the maximum independent set of $G$ is: $12$ $8$ less than $8$ more than $12$
Let $G$ be a simple graph with $20$ vertices and $100$ edges. The size of the minimum vertex cover of G is $8$. Then, the size of the maximum independent set of $G$ is:$1...
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19 votes
3 answers
991
GATE CSE 2005 | Question: 10
Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is: $6$ $8$ $9$ $13$
Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is:$6$$8$$9$$13$
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51 votes
5 answers
993
GATE CSE 2010 | Question: 1
Let $G=(V, E)$ be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in $G.$ If $S$ and $T$ are two different trees with $\xi(S) = \xi(T)$, then $| S| = 2| T |$ $| S | = | T | - 1$ $| S| = | T | $ $| S | = | T| + 1$
Let $G=(V, E)$ be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in $G.$ If $S$ and $T$ are two different trees with ...
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37 votes
7 answers
995
GATE CSE 2004 | Question: 77
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is$2$$3$$4$$5$
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65 votes
9 answers
996
GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-d...
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60 votes
10 answers
997
GATE CSE 2003 | Question: 36
How many perfect matching are there in a complete graph of $6$ vertices? $15$ $24$ $30$ $60$
How many perfect matching are there in a complete graph of $6$ vertices?$15$$24$$30$$60$
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39 votes
8 answers
999
GATE CSE 2002 | Question: 1.25, ISRO2008-30, ISRO2016-6
The maximum number of edges in a $n$-node undirected graph without self loops is $n^2$ $\frac{n(n-1)}{2}$ $n-1$ $\frac{(n+1)(n)}{2}$
The maximum number of edges in a $n$-node undirected graph without self loops is$n^2$$\frac{n(n-1)}{2}$$n-1$$\frac{(n+1)(n)}{2}$
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46 votes
6 answers
1000
GATE CSE 2002 | Question: 1.4
The minimum number of colours required to colour the vertices of a cycle with $n$ nodes in such a way that no two adjacent nodes have the same colour is $2$ $3$ $4$ $n-2 \left \lfloor \frac{n}{2} \right \rfloor+2$
The minimum number of colours required to colour the vertices of a cycle with $n$ nodes in such a way that no two adjacent nodes have the same colour is$2$$3$$4$$n-2 \lef...
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