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Syllabus: Connectivity, Matching, Coloring.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2024-1} &\textbf{2024-2} &\textbf{2023} &\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&0& 1&1&0&0&0.83&1
\\\hline\textbf{2 Marks Count} &1&2&1& 3 &1&0&0&1.33&3
\\\hline\textbf{Total Marks} & 3&5&2&7 &3&0&\bf{0}&\bf{3.33}&\bf{7}\\\hline
\end{array}}}$$

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Recent questions in Graph Theory

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361
Keneth
Are there any graph having chromatic number 1 ??????
Are there any graph having chromatic number 1 ??????
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2 votes
2 answers
362
Graph Theory
The largest possible number of vertices in a graph $G$, with $35$ edges and all vertices are of degree at least $3$ is $24$ $25$ $23$ $26$
The largest possible number of vertices in a graph $G$, with $35$ edges and all vertices are of degree at least $3$ is$24$$25$$23$$26$
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363
Graph Theory DM
In this graph it is said that $a,e,b,c,b$ is a path. But according to definition- in a path vertices and edges can't repeat so why this is a path. confused please clarify.
In this graph it is said that $a,e,b,c,b$ is a path. But according to definition- in a path vertices and edges can't repeat so why this is a path. confused please clarify...
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1 votes
2 answers
364
Graph Theory #self doubt
Can both euler path and euler circuit exist in same graph. Can both Hamiltonian path and Hamiltonian circuit exist in same graph.
Can both euler path and euler circuit exist in same graph.Can both Hamiltonian path and Hamiltonian circuit exist in same graph.
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0 votes
1 answer
365
Clique with one vertex
Is there a clique possible in Graph with one vertex? I mean, is a singleton vertex in itself is a complete sub-graph and can be called a clique.
Is there a clique possible in Graph with one vertex? I mean, is a singleton vertex in itself is a complete sub-graph and can be called a clique.
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1 answer
366
Graph Theory & Permutations
Given 3 connected components with 2,2,3 vertices. In how many ways can we add two edges to connect the whole graph? Also, if possible generalise the method for graph with k connected components each having ni vertices. Ans=84
Given 3 connected components with 2,2,3 vertices. In how many ways can we add two edges to connect the whole graph?Also, if possible generalise the method for graph with ...
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1 votes
2 answers
367
IISc CDS (MTech-R)
Number of distinct simple graphs possible, given 8 vertices and not considering self loops?
Number of distinct simple graphs possible, given 8 vertices and not considering self loops?
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0 votes
1 answer
369
Induction
Prove that the number of edges in a graph with exactly one triangle is at most \begin{align*} \frac{\left( n - 1 \right )^2}{4} + 2 \end{align*}
Prove that the number of edges in a graph with exactly one triangle is at most \begin{align*} \frac{\left( n - 1 \right )^2}{4} + 2\end{align*}
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7 votes
3 answers
370
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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1 votes
1 answer
371
PGEE 2018
Consider Undirected Graph G having vertex V {A,B,C,D,E} and edge pair as E {AB BD BE AC CE CD} A) Given graph is disconnected B) Given graph is complete C) Given graph has vertex connectivity 2 D) Given graph has edge connectivity 1
Consider Undirected Graph Ghaving vertex V {A,B,C,D,E}and edge pair as E {AB BD BE AC CE CD}A) Given graph is disconnectedB) Given graph is completeC) Given graph has ver...
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1 votes
1 answer
374
Narsingh Deo Problem 2-28
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1 votes
1 answer
376
Graph Theory
Let G be a simple graph in which every vertex has degree 3. Prove that G decomposes into claws iff G is bipartite.
Let G be a simple graph in which every vertex has degree 3. Prove that G decomposes into claws iff G is bipartite.
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377
Number of Possible Trees
How many total Homeomorphically Irreducible Trees are possible with 'n' nodes ?
How many total Homeomorphically Irreducible Trees are possible with 'n' nodes ?
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1 answer
378
#Graph Theory Any Simple way to prove this ?
A connected graph ‘G’ may have at most (n–2) cut vertices.
A connected graph ‘G’ may have at most (n–2) cut vertices.
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1 votes
1 answer
379
Graph Book
The maximum number of edges in a n-node undirected graph WITH self-loops is?
The maximum number of edges in a n-node undirected graph WITH self-loops is?
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