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Syllabus: Connectivity, Matching, Coloring.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&1&0&0&1&1&0&1&0&1&0&0.6&1
\\\hline\textbf{2 Marks Count} & 3 &1&0&1&1&1&0&0&0&0&0&0.7&3
\\\hline\textbf{Total Marks} & 7 &3&0&2&3&3&0&1&0&1&\bf{0}&\bf{2}&\bf{7}\\\hline
\end{array}}}$$

Questions without answers in Graph Theory

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3
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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4
Consider a strongly connected directed graph G(V, F), where |V| = 101. The minimum possible value of IEl is
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6
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7
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8
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...
2 votes
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9
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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12
What is a biconnected componenet?Does it always include V-V’ where V’ represent the set of articulation points of a graph G?
1 votes
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13
If G is a simple planar connected graph with 5 vertices, how many edges in maximum can be there in the given graph?
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14
Let Gn be the complete bipartite graph K13, 17 then the chromatic number of G̅n is _____ (G̅n is complement of Gn and n = 30)A13B17Cn(n−1)2−13×17Dn(n−1)2−2
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15
If [P(A); ⊆] is a lattice where A = {x, y} and P(A) is the power set then what is the sum of element in Greatest Lower Bound (GLB) set of given lattice?x + y xy0
3 votes
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16
Let $G=(V,E)$ where $V=\left \{ 1,2,3,4,.....,150\right \}$ and $(u,v) \in E$ if either $(u mod v) =0$ or $(v mod u)=0$.The Chromatic number of G is ?
3 votes
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17
1 votes
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18
Given a tree $\text{T}$ and $\lambda \geq 2$ colours $\left(c_{1}, c_{2}, \ldots, c_{\lambda}\right),$ how many proper colourings of the tree $\text{T}$ are possible?
1 votes
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19
1 votes
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20
1 votes
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23
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25
6 votes
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26
Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$
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27
What is Graph Decomposition & is it in the syllabus?If it is then please can anyone share some online resources for it. Thank you.
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28
What is meant by edge disjoint hamiltonian circuits in a graph
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29
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30
Given a sequence $a_1$, $a_2$ , $a_3$ ... $a_n$ of any different positive integers, exhibit an arrangement of integers between 1 and $n^2$ which has no increasing or decr...
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