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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

9 votes
4 answers
151
GATE CSE 1992 | Question: 02,viii
A non-planar graph with minimum number of vertices has $9$ edges, $6$ vertices $6$ edges, $4$ vertices $10$ edges, $5$ vertices $9$ edges, $5$ vertices
A non-planar graph with minimum number of vertices has$9$ edges, $6$ vertices$6$ edges, $4$ vertices$10$ edges, $5$ vertices$9$ edges, $5$ vertices
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4 votes
2 answers
152
Graph Coloring
How many ways are there to color this graph from any $4$ of the following colors : Violet, Indigo, Blue, Green, Yellow, Orange and Red ? There is a condition that adjacent vertices should not be of the same color I am getting $1680$. Is it correct?
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0 votes
4 answers
153
NIELIT 2017 July Scientist B (CS) - Section B: 14
If $G$ is an undirected planar graph on $n$ vertices with $e$ edges then $e\leq n$ $e\leq 2n$ $e\leq 3n$ None of the option
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2 votes
1 answer
158
GATE Overflow Test Series | Mock GATE | Test 6 | Question: 13
A simple graph $G$ has degree sequence $(7,7,6,5,5,4,3,3,2)$. What is the degree sequence of $G^{c}$? $(2,3,3,4,5,5,6,7,7)$ $(1,1,3,3,4,5,5,6,6)$ $(1,1,2,3,3,4,5,5,6)$ $(2,2,3,4,4,5,6,6,7)$
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1 votes
0 answers
159
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?
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0 votes
2 answers
160
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
161
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
162
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?
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1 votes
1 answer
163
Testbook Test Series
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1 votes
3 answers
165
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.
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3 votes
2 answers
167
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
168
ISRO2018-38
The number of edges in a regular graph of degree: $d$ and $n$ vertices is: maximum of $n$ and $d$ $n +d$ $nd$ $nd/2$
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2 votes
2 answers
170
GATE Overflow Test Series | Discrete Mathematics | Test 4 | Question: 9
What is the smallest number of colors that can be used to color the vertices of a cube so that no two adjacent vertices are colored identically?
What is the smallest number of colors that can be used to color the vertices of a cube so that no two adjacent vertices are colored identically?
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