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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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Hot questions in Graph Theory

1 votes
0 answers
153
Made Easy Full length Test
Options Given were---- ADC ABC Both the above None of these According to me the answer should be {A,B,C,D} as this is the largest set and every node is capable to reach every other node.. but the answer given was option C so can anyone plz tell me whats the correct answer?
Options Given were ADCABCBoth the aboveNone of these According to me the answer should be {A,B,C,D} as this is the largest set and every node is capable to reach every o...
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0 votes
2 answers
154
self doubt
Both euler path and euler circuit can be present in a graph ?
Both euler path and euler circuit can be present in a graph ?
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0 votes
2 answers
155
Self Doubt
Why is the vertex connectivity of a graph always less than or equal to its edge connectivity?
Why is the vertex connectivity of a graph always less than or equal to its edge connectivity?
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2 votes
2 answers
156
Seld doubt DM
Consider a tree T with n vertices and (n – 1) edges. We define a term called cyclic cardinality of a tree (T) as the number of cycles created when any two vertices of T are joined by an edge. Given a tree with 10 vertices, what is the cyclic cardinality of this tree?
Consider a tree T with n vertices and (n – 1) edges. We define a term called cyclic cardinality of a tree (T) as the number of cycles created when any two vertices of T...
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1 votes
1 answer
157
Testbook Test Series
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1 votes
3 answers
159
No of spanning Trees
Let $K_n$ denote the complete undirected graph with $n$ vertices where n is an even number. Find the maximum number of spanning trees of $K_n$ that can be formed in such a way that no two of these spanning trees have a common edge.
Let $K_n$ denote the complete undirected graph with $n$ vertices where n is an even number. Find the maximum number of spanning trees of $K_n$ that can be formed in such ...
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3 votes
2 answers
161
Spannig trees
For a complete graph with 10 vertices, The number of spanning trees is at least_____?
For a complete graph with 10 vertices, The number of spanning trees is at least_____?
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7 votes
3 answers
162
ISRO2018-38
The number of edges in a regular graph of degree: $d$ and $n$ vertices is: maximum of $n$ and $d$ $n +d$ $nd$ $nd/2$
The number of edges in a regular graph of degree: $d$ and $n$ vertices is:maximum of $n$ and $d$ $n +d$$nd$$nd/2$
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37 votes
7 answers
165
GATE IT 2006 | Question: 11
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a Hamiltonian cycle grid hypercube tree
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is aHamiltonian cyclegri...
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1 votes
1 answer
166
NIELIT 2017 July Scientist B (IT) - Section B: 8
A connected planar graph divides the plane into a number of regions. If the graph has eight vertices and these are linked by $13$ edges, then the number of regions is: $5$ $6$ $7$ $8$
A connected planar graph divides the plane into a number of regions. If the graph has eight vertices and these are linked by $13$ edges, then the number of regions is:$5$...
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3 votes
3 answers
167
JEST2020
Let G(V,E) be a simple graph. Let G’(V,E’) be a graph obtained from G such that (u,v) is an edge in G’ if (u,v) is not an edge in G. Which of the following is true? At least one of G or G’ are connected. G is necessarily disconnected. Both G and G’ are disconnected. None of the above.
Let G(V,E) be a simple graph. Let G’(V,E’) be a graph obtained from G such that (u,v) is an edge in G’ if (u,v) is not an edge in G. Which of the following is true?...
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34 votes
4 answers
170
GATE IT 2008 | Question: 3
What is the chromatic number of the following graph? $2$ $3$ $4$ $5$
What is the chromatic number of the following graph? $2$$3$$4$$5$
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