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Recent questions tagged degree-of-graph

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GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 15
Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , ... the following can be the degree of the last vertex? (Select all that are possible)0348
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TIFR CSE 2023 | Part B | Question: 10
A $d$-regular graph is one in which every vertex has degree $d$. Also, a minimum cut in a graph is a smallest set of edges which, upon removal, disconnects the ... Which of the following must be the size of this minimum cut?$0$1$2$3$4$
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Degree sequence of graph
Someone please solve it.
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NIELIT Scientific Assistant A 2020 November: 96
In an undirected graph, if we add the degrees of all vertices, it is:oddevencannot be determinedalways $n+1,$ where $n$ is number of nodes
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NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 7
The number of the edges in a regular graph of degree $’d’$ and $’n’$ vertices is Maximum of $n,d$n+d$nd$nd/2$
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NIELIT 2016 MAR Scientist B - Section B: 3
Maximum degree of any node in a simple graph with $n$ vertices is$n-1$n$n/2$n-2$
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NIELIT 2017 July Scientist B (IT) - Section B: 1
Given an undirected graph $G$ with $V$ vertices and $E$ edges, the sum of the degrees of all vertices is$E$2E$V$2V$
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NIELIT 2017 July Scientist B (CS) - Section B: 2
Which of the following statements is/are TRUE for an undirected graph?Number of odd degree vertices is evenSum of degrees of all vertices is evenP onlyQ onlyBoth P and QNeither P nor Q
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Zeal Test Series 2019: Graph Theory - Degree Of Graph
A simple graph is one in which there are no self loops and each pair of distinct vertices is connected by at most one edge. Let G be a simple graph on 8 ... of degree 7. Which of the following can be the degree of the last vertex ____ ?
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Graph Theory Doubt
If there are exactly 2 vertices x and y of odd degree in a graph G, then there must be a path between x and y,Is this true? Please explain with valid reasons.
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TIFR CSE 2019 | Part B | Question: 3
A graph is $d$ - regular if every vertex has degree $d$. For a $d$ - regular graph on $n$ vertices, which of the following must be TRUE?$d$ divides $n$Both $d$ and ... oddAt least one of $d$ and $n$ is oddAt least one of $d$ and $n$ is even
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TIFR CSE 2018 | Part B | Question: 8
In an undirected graph $G$ with $n$ vertices, vertex $1$ has degree $1$, while each vertex $2,\ldots,n-1$ has degree $10$ and the degree of vertex $n$ is ... of the graph is at most $\frac{n}{10}$All of the above choices must be TRUE
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Graph Degree sequence : Bondy and Murty : $1.1.16$
Let $d = (d_1,d_2,\dots, d_n)$ be a nonincreasing sequence of nonnegative integers, that is, $d_1 \geq d_2 \geq · · · \geq d_n \geq 0$. Show that:there is a loopless graph ... if $\sum_{i=1}^{n}d_i$ is even and $d_1 \leq \sum_{i=2}^{n}d_i$
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GATE CSE 2017 Set 2 | Question: 23
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
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GATE CSE 1987 | Question: 9c
Show that the number of odd-degree vertices in a finite graph is even.
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ISRO2009-52
If $\text{G}$ is a graph with e edges and n vertices the sum of the degrees of all vertices in $\text{G}$ is$e$e/2$e^2$2 e$
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CMI2015-A-05
An undirected graph has $10$ vertices labelled $1, 2,\dots , 10$ and $37$ edges. Vertices $1, 3, 5, 7, 9$ have degree $8$ and vertices $2, 4, 6, 8$ have degree $7.$ What is the degree of vertex $10$ ?$5$6$ $7$ $8$
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CMI2013-A-06
A simple graph is one in which there are no self-loops and each pair of distinct vertices is connected by at most one edge. Let $G$ be a simple graph on $8$ ... $. Which of the following can be the degree of the last vertex?$3$0$5$4$
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