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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

1 votes
1 answer
422
Graph theory
As a triangle graph is $2 -$ connected, thus for a given triangle graph, $r= 2( r_1\text{ and } r_2)$ , $k=2, e = 3, v=3$, but it still doesn't satisfy the equation, Can someone tell me where did I go wrong? Thanks
As a triangle graph is $2 -$ connected, thus for a given triangle graph, $r= 2( r_1\text{ and } r_2)$ , $k=2, e = 3, v=3$, but it still doesn't satisfy the equation, Can ...
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0 votes
0 answers
423
[Graphs]IIT-k Written test
Graph Matching was explained. Let $S$ and $R$ be the matching graph, then a new graph $G=(S-R) \cup (R-S)$, will be union of vertex disjoint path and cycle. Also prove that the cycle obtained will be of even length.
Graph Matching was explained. Let $S$ and $R$ be the matching graph, then a new graph $G=(S-R) \cup (R-S)$, will be union of vertex disjoint path and cycle. Also prove th...
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2 votes
0 answers
424
[Graphs]IIT-k Written test
if degree of vertices < 3, then prove that the graph will be union of vertex disjoint path and cycle
if degree of vertices < 3, then prove that the graph will be union of vertex disjoint path and cycle
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0 votes
1 answer
425
Rosen (Graph)
Show that an edge in a simple graph is a cut edge if and only if this edge is not a part of any simple circuit in the graph.
Show that an edge in a simple graph is a cut edge if and only if this edge is not a part of any simple circuit in the graph.
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0 votes
1 answer
426
Kenneth Rosen Edition 6th Exercise 8.4 Question 70 (Page No. 565 )
How much storage is needed to represent a simple graph with n vertices and m edges using. a) adjacency lists? b) an adjacency matrix? c) an incidence matrix?
How much storage is needed to represent a simple graph with n vertices and m edges using.a) adjacency lists?b) an adjacency matrix?c) an incidence matrix?
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1 votes
0 answers
427
[2016]IITK interview question
1. Prove/Disprove: a) If a graph has k-independent components, it it n-k+1 colorable b) converse of (a) c) If a graph is not n-1 colorable, it's a clique
1. Prove/Disprove:a) If a graph has k-independent components, it it n-k+1 colorableb) converse of (a)c) If a graph is not n-1 colorable, it's a clique
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0 votes
0 answers
428
Graph theory
What is unorderd and ordered (if any) cycles in a given graph?
What is unorderd and ordered (if any) cycles in a given graph?
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32 votes
5 answers
429
GATE CSE 2018 | Question: 18
The chromatic number of the following graph is _____
The chromatic number of the following graph is _____
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3 votes
3 answers
433
Ace Test Series: Graph Theory - Number Of Spanning Trees
How to approach such questions ? Please provide detailed solution. Answer given is option C
How to approach such questions ? Please provide detailed solution. Answer given is option C
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0 votes
2 answers
434
discrete maths
How many ordered pair of integers (a, b) are needed to guarantee that there are two ordered pairs (a1, b1) and (a2, b1) such that a1 mod 5 = a2 mod 5 and b1 mod 5 = b2 mod 5? should not answer be 25 here
How many ordered pair of integers (a, b) are needed to guarantee that there are two ordered pairs (a1, b1) and (a2, b1) such that a1 mod 5 = a2 mod 5 and b1 mod 5 = b2 mo...
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0 votes
1 answer
435
discrete maths
Consider the following statements: S1: Every cyclic group is Abelian group. S2: Every Abelian group is cyclic group. S3: Cyclic group of order 10 have 4 generators. Which of the following is true?
Consider the following statements:S1: Every cyclic group is Abelian group.S2: Every Abelian group is cyclic group.S3: Cyclic group of order 10 have 4 generators.Which of ...
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0 votes
1 answer
436
Test series
Plz explain ??
Plz explain ??
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1 votes
0 answers
437
Test series
my doubt is why 14 has been subtracted ??
my doubt is why 14 has been subtracted ??
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1 votes
0 answers
438
MadeEasy Test Series: Graph Theory - Vertex Cover
Vertex cover = Total vertex - Maximum independent set vertex cover = 8 - 3 = 5. In given answer Covering number is given as 4. I think it is given wrong please verify. Thank you.
Vertex cover = Total vertex - Maximum independent setvertex cover = 8 - 3 = 5.In given answer Covering number is given as 4. I think it is given wrong please verify. Than...
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