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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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Questions without an upvoted answer in Graph Theory

0 votes
1 answer
1
ISI kolkata MTech CS 2019
Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths from $u$ to $v$ that do not contain the vertex $w$.
Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths fro...
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6
Consider a weighted undirected graph with positive edge weights and let (u, v) be an [2] edge in the graph. It is known that the shortest path from source vertex r to u has weight 53 and shortest path from r to v has weight 65. Which statement is always true?
Consider a weighted undirected graph with positive edge weights and let (u, v) be an edge in the graph. It is known that the shortest path from source vertex r to u hasw...
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7
ISRO 2024
Maximum number of Simple graphs possible with $n$ vertices $2^{n(n-1)/2}$ $2^{(n-1)/2}$ $2^{n(n+1)/2}$ $2^{n(n+1)}$
Maximum number of Simple graphs possible with $n$ vertices$2^{n(n-1)/2}$$2^{(n-1)/2}$$2^{n(n+1)/2}$$2^{n(n+1)}$
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8
ISRO 2024
If there are five faces and nine vertices in an undirected planar graph, then number of edges is 14 6 12 None of the above
If there are five faces and nine vertices in an undirected planar graph, then number of edges is14612None of the above
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10
Made easy test series
Consider a strongly connected directed graph G(V, F), where |V| = 101. The minimum possible value of IEl is
Consider a strongly connected directed graph G(V, F), where |V| = 101. The minimum possible value of IEl is
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13
Find the MIS and MaxIS
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14
#self doubt
Domination set and MIS are the same?
Domination set and MIS are the same?
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15
Regular and complete graph
which of the following statements is true: a complete graph is $(N-1)$ regular a $(N-1)$ regular is a complete graph
which of the following statements is true:a complete graph is $(N-1)$ regulara $(N-1)$ regular is a complete graph
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16
#self_doubt#pyq#graphtheory
Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to the answer is 45 but for the following cases, what will be the answer? 1- if the graph is directed 2- if vertices are not labeled.
Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal tothe answer is 45 but for ...
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17
made easy test series
Suppose A is a 12 by 9 incidence matrix from a connected (but unknown) graph with 12 edges and 9 nodes. Then how many columns of A are independent? what this question want to ask can someone help me {hint}
Suppose A is a 12 by 9 incidence matrix from a connected (but unknown) graph with 12 edges and 9 nodes. Then how many columns of A are independent?what this question want...
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18
#applied course
how many regions are in the above graph and please explain with region formula also. r=e-v+(c+1) my attempt is : r=5-5+2 r=2 but the rule is twice the no of boundary edges which is (5*2) = sum of region degrees which (4+5=9 ) can someone explain where the fault is
how many regions are in the above graph and please explain with region formula also.r=e-v+(c+1)my attempt is :r=5-5+2r=2but the rule is twice the no of boundary edges whi...
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2 votes
1 answer
20
Chromatic Number
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22
#Graph Theory
Prove that following graph does not have Hamiltonian cycle.
Prove that following graph does not have Hamiltonian cycle.
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23
What is Kurawtoski Graph?
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24
Graph theory self doubt
Number of hamiltonian cycles for a graph K 5, 5( bipartite graph ) ??
Number of hamiltonian cycles for a graph K 5, 5( bipartite graph ) ??
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25
Planar Graphs | Graph Theory | Selfdoubt
In a Connected Planar Bipartite Graph of order 10 atmost how many edges be present ?
In a Connected Planar Bipartite Graph of order 10 atmost how many edges be present ?
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1 votes
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26
Self Made Question
Consider a connected undirected graph G with n vertices, where n > 4. Suppose that G has the property that every vertex has a degree of at least n/2, i.e., deg(v) ≥ n/2 for all vertices v in G. Prove that G must contain a cycle of length at most 3n/4.
Consider a connected undirected graph G with n vertices, where n 4. Suppose that G has the property that every vertex has a degree of at least n/2, i.e., deg(v) ≥ n/2 ...
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2 votes
0 answers
29
discrete mathematics
The maximum number of edges possible in a graph G with 9 vertices which is 3 colourable is equal to A 24 B 27 C 36 D None of the above
The maximum number of edges possible in a graph G with 9 vertices which is 3 colourable is equal toA 24B 27C 36D None of the above
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