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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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Most answered questions in Graph Theory

6 votes
3 answers
124
IIT Kanpur Written Test
There are 16072016 users in Facebook. A graph is formed where an edge(u,v) is defined when a male is friend to a female and vice versa. Estimate the number of simple cycle of length 1607 formed in the graph?
There are 16072016 users in Facebook. A graph is formed where an edge(u,v) is defined when a male is friend to a female and vice versa. Estimate the number of simple cycl...
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4 votes
3 answers
125
UGC NET CSE | September 2013 | Part 2 | Question: 8
Consider an undirected graph G with 100 nodes. The maximum number of edges to be included in G so that the graph is not connected is 2451 4950 4851 9900
Consider an undirected graph G with 100 nodes. The maximum number of edges to be included in G so that the graph is not connected is2451495048519900
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4 votes
3 answers
126
UGC NET CSE | June 2012 | Part 3 | Question: 72
$G_1$ and $G_2$ are two graphs as shown: Both $G_1$ and $G_2$ are planar graphs Both $G_1$ and $G_2$ are not planar graphs $G_1$ is planar and $G_2$ is not planar $G_1$ is not planar and $G_2$ is planar
$G_1$ and $G_2$ are two graphs as shown:Both $G_1$ and $G_2$ are planar graphsBoth $G_1$ and $G_2$ are not planar graphs$G_1$ is planar and $G_2$ is not planar$G_1$ is no...
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8 votes
3 answers
127
ISRO2009-56
A simple graph ( a graph without parallel edge or loops) with $n$ vertices and $k$ components can have at most $n$ edges $n-k$ edges $(n-k) (n-k+1)$ edges $(n-k) (n-k+1)/2$ edges
A simple graph ( a graph without parallel edge or loops) with $n$ vertices and $k$ components can have at most$n$ edges$n-k$ edges$(n-k) (n-k+1)$ edges$(n-k) (n-k+1)/2$ e...
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7 votes
3 answers
128
ISRO2009-55
In a graph $\text{G}$ there is one and only one path between every pair of vertices then $\text{G}$ is a Path Walk Tree Circuit
In a graph $\text{G}$ there is one and only one path between every pair of vertices then $\text{G}$ is aPathWalkTreeCircuit
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3 votes
3 answers
129
UGC NET CSE | June 2013 | Part 2 | Question: 37
Which of the following connected graph has exactly one spanning tree? Complete graph Hamiltonian graph Euler graph None of the above
Which of the following connected graph has exactly one spanning tree? Complete graph Hamiltonian graph Euler graph None of the above
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1 votes
3 answers
130
k 3,4 graph
The graph $K_{3,4}$ has 3 edges 4 edges 7 edges 12 edges
The graph $K_{3,4}$ has3 edges4 edges7 edges12 edges
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2 votes
3 answers
132
N cube Graph
In N-cube graph we have no. of vertices = $2^N$ and no. of edges = $N*2^{N-1}$ Can anyone explain how we get this no. of edges?
In N-cube graph we have no. of vertices = $2^N$ and no. of edges = $N*2^{N-1}$Can anyone explain how we get this no. of edges?
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0 votes
3 answers
133
The number of colors needed to edge color a simple graph with maximum degree Δ is?
The number of colors needed to edge color a simple graph with maximum degree Δ is? Is this there in portion?
The number of colors needed to edge color a simple graph with maximum degree Δ is?Is this there in portion?
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1 votes
3 answers
136
Find maximum edges in Graph
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3 votes
3 answers
137
Number of nodes of distinct degree
In a simple connected undirected graph with n nodes(where n≧2), The maximum number of nodes with distinct degrees is n-1 n-2 n-3 2
In a simple connected undirected graph with n nodes(where n≧2), The maximum number of nodes with distinct degrees is n-1n-2n-32
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6 votes
3 answers
138
How to find no of paths of length 2 in the below graph ?
Determine the number of paths of length $2$ in the following graph I couldn't get this logic .
Determine the number of paths of length $2$ in the following graphI couldn't get this logic .
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48 votes
3 answers
139
GATE CSE 1991 | Question: 16-b
Show that all vertices in an undirected finite graph cannot have distinct degrees, if the graph has at least two vertices.
Show that all vertices in an undirected finite graph cannot have distinct degrees, if the graph has at least two vertices.
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