GATE Overflow - Recent questions in Graph Theory
https://db.gateoverflow.in/questions/mathematics/discrete-mathematics/graph-theory
Powered by Question2AnswerGateForum Question Bank :Graph Theory
https://db.gateoverflow.in/312467/gateforum-question-bank-graph-theory
<p>What is the probability that there is an edge in an undirected random graph having 8 vertices?</p>
<ol style="list-style-type:lower-alpha" type="a">
<li>1</li>
<li> 1/8 </li>
</ol>Graph Theoryhttps://db.gateoverflow.in/312467/gateforum-question-bank-graph-theorySun, 19 May 2019 16:52:25 +0000ACE Workbook:
https://db.gateoverflow.in/311969/ace-workbook
ACE Workbook:<br />
<br />
Q) Let G be a simple graph(connected) with minimum number of edges. If G has n vertices with degree-1,2 vertices of degree 2, 4 vertices of degree 3 and 3 vertices of degree-4, then value of n is ? Can anyone give the answer and how to approach these problems. Thanks in advance.Graph Theoryhttps://db.gateoverflow.in/311969/ace-workbookSun, 12 May 2019 16:32:08 +0000Difference between DAG and Multi-stage graph
https://db.gateoverflow.in/310910/difference-between-dag-and-multi-stage-graph
I have trouble understanding the difference between DAG and Multi-stage graph. I know what each of them is<br />
<br />
But I think that a multi-stage graph is also a DAG. Are multi-stage graphs a special kind of DAG?Graph Theoryhttps://db.gateoverflow.in/310910/difference-between-dag-and-multi-stage-graphSun, 28 Apr 2019 10:55:21 +0000ISI2017-PCB-B-1(b)
https://db.gateoverflow.in/309300/isi2017-pcb-b-1-b
Show that if the edge set of the graph $G(V,E)$ with $n$ nodes can be partitioned into $2$ trees, then there is at least one vertex of degree less than $4$ in $G$.Graph Theoryhttps://db.gateoverflow.in/309300/isi2017-pcb-b-1-bMon, 08 Apr 2019 03:51:58 +0000self-doubt
https://db.gateoverflow.in/308120/self-doubt
A graph with alternating edges and vertices is called a walk (we can repeat the number of vertices and edges any number of times) .<br />
<br />
A walk in which no edges are repeated is called a trial.<br />
<br />
A trial in which no vertices are repeated is called a path.<br />
<br />
A trial in which only the starting and ending vertices are repeated is called a circuit.<br />
<br />
Are the definitions correct??Graph Theoryhttps://db.gateoverflow.in/308120/self-doubtSun, 31 Mar 2019 14:33:41 +0000self doubt
https://db.gateoverflow.in/308053/self-doubt
What is the general formula for number of simple graph having n unlabelled vertices ??Graph Theoryhttps://db.gateoverflow.in/308053/self-doubtSun, 31 Mar 2019 04:50:32 +0000Allen Career Institute: Spanning tree
https://db.gateoverflow.in/307803/allen-career-institute-spanning-tree
<table style="width:100%">
<tbody>
<tr>
<td style="vertical-align:center">
<p>Let $G$ be a simple undirected complete and weighted graph with vertex set $V = {0, 1, 2, …. 99.}$ Weight of the edge $(u, v)$ is $\left | u-v \right |$ where $0\leq u, v\leq 99$ and $u\neq v$. Weight of the corresponding maximum weighted spanning tree is______________</p>
</td>
</tr>
</tbody>
</table>
<hr>
<p>Doubt:Here asking for maximum weight spanning tree. So, there weight will be $0$ to every node. Isnot it? but answer given 7351. </p>Graph Theoryhttps://db.gateoverflow.in/307803/allen-career-institute-spanning-treeFri, 29 Mar 2019 07:10:51 +0000Allen Career Institute:Graph Theory
https://db.gateoverflow.in/307742/allen-career-institute-graph-theory
If G be connected planar graph with 12 vertices of deg 4 each. In how many regions can this planar graph be partitioned?Graph Theoryhttps://db.gateoverflow.in/307742/allen-career-institute-graph-theoryThu, 28 Mar 2019 09:21:28 +0000Graph Decomposition
https://db.gateoverflow.in/306350/graph-decomposition
What is Graph Decomposition & is it in the syllabus?<br />
<br />
If it is then please can anyone share some online resources for it. Thank you.Graph Theoryhttps://db.gateoverflow.in/306350/graph-decompositionSun, 17 Mar 2019 05:33:28 +0000Narsingh deo
https://db.gateoverflow.in/305308/narsingh-deo
What is meant by edge disjoint hamiltonian circuits in a graphGraph Theoryhttps://db.gateoverflow.in/305308/narsingh-deoMon, 04 Mar 2019 20:29:26 +0000JEST 2019
https://db.gateoverflow.in/304353/jest-2019
A directed graph with n vertices, in which each vertex has exactly 3 outgoing edges. Which one is true?<br />
<br />
A) All the vertices have indegree = 3 .<br />
<br />
B) Some vertices will have indegree exactly 3.<br />
<br />
C)Some vertices have indegree atleast 3.<br />
<br />
D) Some of the vertices have indegree atmost 3Graph Theoryhttps://db.gateoverflow.in/304353/jest-2019Mon, 18 Feb 2019 04:54:43 +0000JEST 2019 Descriptive Q2 (8 Marks)
https://db.gateoverflow.in/304302/jest-2019-descriptive-q2-8-marks
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 decreasing subsequence of length n+1.Graph Theoryhttps://db.gateoverflow.in/304302/jest-2019-descriptive-q2-8-marksSun, 17 Feb 2019 09:42:20 +0000JEST 2019 Descriptive Q1 (8 Marks)
https://db.gateoverflow.in/304294/jest-2019-descriptive-q1-8-marks
Suppose that G contains a cycle C, and a path of length at least k between some two<br />
vertices of C. Show that G contains a cycle of length at least √k.Graph Theoryhttps://db.gateoverflow.in/304294/jest-2019-descriptive-q1-8-marksSun, 17 Feb 2019 08:53:25 +0000GATE2019-12
https://db.gateoverflow.in/302836/gate2019-12
<p>Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to</p>
<ol style="list-style-type:upper-alpha">
<li>$n!$</li>
<li>$(n-1)!$</li>
<li>$1$</li>
<li>$\frac{(n-1)!}{2}$</li>
</ol>Graph Theoryhttps://db.gateoverflow.in/302836/gate2019-12Thu, 07 Feb 2019 09:40:52 +0000GATE2019-38
https://db.gateoverflow.in/302810/gate2019-38
<p>Let $G$ be any connected, weighted, undirected graph.</p>
<ol style="list-style-type:upper-roman">
<li>$G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight.</li>
<li>$G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut.</li>
</ol>
<p>Which of the following statements is/are TRUE?</p>
<ol style="list-style-type:upper-alpha">
<li>I only</li>
<li>II only</li>
<li>Both I and II</li>
<li>Neither I nor II</li>
</ol>Graph Theoryhttps://db.gateoverflow.in/302810/gate2019-38Thu, 07 Feb 2019 09:40:42 +0000GATE 2019 8
https://db.gateoverflow.in/302770/gate-2019-8
Q.8 Let G be an undirected complete graph on n vertices, where n > 2. Then, the number of different Hamiltonian cycles in G is equal to<br />
<br />
1. (n-1)!/2<br />
<br />
2. 1<br />
<br />
3.(n-1)!<br />
<br />
4. n!Graph Theoryhttps://db.gateoverflow.in/302770/gate-2019-8Thu, 07 Feb 2019 08:24:34 +0000GATE2019
https://db.gateoverflow.in/301872/gate2019
What is the total number of different Hamiltonian cycles for the complete graph of n vertices?Graph Theoryhttps://db.gateoverflow.in/301872/gate2019Sun, 03 Feb 2019 08:54:57 +0000Abelian group
https://db.gateoverflow.in/301807/abelian-group
A quick question <br />
<br />
Is every multiplication modulo function a Abelian group....Or is it the case that the function should have prime number as moduloGraph Theoryhttps://db.gateoverflow.in/301807/abelian-groupSat, 02 Feb 2019 04:23:16 +0000GeeksforGeeks
https://db.gateoverflow.in/301391/geeksforgeeks
<div class="panel panel-default" style="margin:5px;background-color:#f5f5f5">
<div class="problemQuestion panel-body" style="font-weight: 700;padding:10px;margin:20px;font-size:15px;">Let G be a graph with no isolated vertices, and let M be a maximum matching of G. For each vertex v not saturated by M, choose an edge incident to v. Let T be the set of all the chosen edges, and let L = M ∪ T. Which of the following option is TRUE?</div>
</div>
<div style="margin-left:20px;margin-top:15px;">
<div class="table-responsive">
<table>
<tbody>
<tr>
<td style="width:30px">
<div style="color: #fff;background: #00930E;width: 40px;height: 40px;display: block; border-radius: 40px; -moz-border-radius: 40px; -webkit-border-radius: 40px; -khtml-border-radius: 40px; font-size: 30px; line-height: 40px; text-decoration: none; text-align: center; font-family: Arial,Helvetica,">A</div>
</td>
<td><strong>L is always an edge cover of G.</strong></td>
</tr>
<tr>
<td style="width:30px">
<div style="color: #fff;background: #00930E;width: 40px;height: 40px;display: block; border-radius: 40px; -moz-border-radius: 40px; -webkit-border-radius: 40px; -khtml-border-radius: 40px; font-size: 30px; line-height: 40px; text-decoration: none; text-align: center; font-family: Arial,Helvetica,">B</div>
</td>
<td><strong>L is always a minimum edge cover of G.</strong></td>
</tr>
<tr>
<td style="width:30px">
<div style="color: #fff;background: #00930E;width: 40px;height: 40px;display: block; border-radius: 40px; -moz-border-radius: 40px; -webkit-border-radius: 40px; -khtml-border-radius: 40px; font-size: 30px; line-height: 40px; text-decoration: none; text-align: center; font-family: Arial,Helvetica,">C</div>
</td>
<td><strong>Both (A) and (B)</strong></td>
</tr>
<tr>
<td style="width:30px">
<div style="color: #fff;background: #00930E;width: 40px;height: 40px;display: block; border-radius: 40px; -moz-border-radius: 40px; -webkit-border-radius: 40px; -khtml-border-radius: 40px; font-size: 30px; line-height: 40px; text-decoration: none; text-align: center; font-family: Arial,Helvetica,">D</div>
</td>
<td><strong>Neither (A) nor (B)</strong></td>
</tr>
</tbody>
</table>
</div>
</div>
<p> </p>
<p>Can anyone pls help solving this?</p>Graph Theoryhttps://db.gateoverflow.in/301391/geeksforgeeksWed, 30 Jan 2019 16:42:45 +0000Madeeasy
https://db.gateoverflow.in/301104/madeeasy
A graph G is called self complementary iff G is isomorphic to its complement. Let X be a self complementary graph. Which of the following is a viable possibility with regards to the connectivity of X and X', where X' denotes the complement of X, <br />
<br />
Option a) Both must be disconnected<br />
<br />
b) X is connected X’ disconnected<br />
<br />
c)X is disconnected and X’ connected<br />
<br />
d)both are connected<br />
<br />
answer d<br />
<br />
I just want to verify this explanation before assuming that it is correct.<br />
<br />
solution given by them<br />
<br />
Firstly we know that if two graphs Gi and G, are isomorphic, then either both of them will be connec.d, or both will be disconnected, and it's easy t gue that a situation like option (b) and (c) can never happen as they are isomorphic. Now the option (a) violates the theorem "at least one of G and G' must be connected" so (a) is also ruled out. So the only viable possibility is option (d). Note that a question based on this concept can probably come M GATE, and they can frame it as "Every self complementary graph is corunected" or "Some self complementary graphs are discormected". So be prepared to answer such questions. So the conclusion is "Every sell complementary graph is cormected". So option (d) is the correct answer.Graph Theoryhttps://db.gateoverflow.in/301104/madeeasyTue, 29 Jan 2019 17:04:11 +0000selfdoubt-ME-testseries
https://db.gateoverflow.in/300972/selfdoubt-me-testseries
<p>we define a new measure ,called GoldIndex(G,C).it takes two arguments as input namely a graph G and set of colors C respectively . the subroutine outputs an integer denoting the number of ways assigning colors to vertices in G such that at least two vertices in G have the same color.Let $k_n$ denote the complete graph having n vertices respectively and C={red,green,blue ,yellow}.then the GoldIndex ($k_3,C$) will be equal to_</p>
<p>my attempt –</p>
<p>the number of ways assigning colors to vertices in G such that at least two vertices in G have the same color= two vertices have same colors + three vertices have same colors (because $K_3$)</p>
<p>two vertices have same colors=$\binom{4}{2}$*3 // first choosing two colors out of four and then assigning these two colors on three vertices </p>
<p>three vertices have same colors (because $K_3$)=$\binom{4}{3}$*1 // first choosing three colors out of four and then assigning these three colors on three vertices so only one way</p>
<p>so total no. of ways =18+4 =22</p>
<p>i don’t know where m i going wrong ,please help me-</p>
<hr>
<p>i know their solution is correct but i want to verify my approach-</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=16384660421664919612"></p>Graph Theoryhttps://db.gateoverflow.in/300972/selfdoubt-me-testseriesTue, 29 Jan 2019 11:56:58 +0000#GRAPH THEORY
https://db.gateoverflow.in/300870/%23graph-theory
<p>A simple <strong>regula</strong>r graph n vertices and 24 edges, find all possible values of n.</p>Graph Theoryhttps://db.gateoverflow.in/300870/%23graph-theoryTue, 29 Jan 2019 05:01:28 +0000max weighted MST possible
https://db.gateoverflow.in/299680/max-weighted-mst-possible
<p><strong> Let G be a complete undirected graph on 5 vertices 10 edges, with weights being 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Let X be the value of the maximum possible weight a MST of G can have. Then the value of x will be_____</strong></p>
<p>
<br>
the answer to this question is given as 11 but there is no procedure given . Please ,can anyone help me out in understanding the procedure</p>Graph Theoryhttps://db.gateoverflow.in/299680/max-weighted-mst-possibleFri, 25 Jan 2019 19:22:19 +0000Made Easy Practice Book
https://db.gateoverflow.in/299653/made-easy-practice-book
<ul>
<li>
<p>The number of labelled subgraph possible for the graph given below are ________.</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=16011923614650325494"></p>
</li>
</ul>Graph Theoryhttps://db.gateoverflow.in/299653/made-easy-practice-bookFri, 25 Jan 2019 18:14:13 +0000Counting
https://db.gateoverflow.in/299582/counting
<p><img alt="" height="832" src="https://gateoverflow.in/?qa=blob&qa_blobid=2326657456942833462" width="416"></p>
<hr>Graph Theoryhttps://db.gateoverflow.in/299582/countingFri, 25 Jan 2019 15:28:38 +0000SelfDoubt
https://db.gateoverflow.in/299342/selfdoubt
A graph with each vertex has even degree contain Hamiltonian Cycle.<br />
<br />
True/False plz explain how to ensure Hamiltonian Cycle.Graph Theoryhttps://db.gateoverflow.in/299342/selfdoubtFri, 25 Jan 2019 04:18:21 +0000Virtual Gate
https://db.gateoverflow.in/299135/virtual-gate
A complete graph on n vertices is an undirected graph in which every pair of distinct vertices is connected by an edge. A simple path in a graph is one in which no vertex is repeated. Let G be a complete graph on 10 vertices. Let u, v, w be three distinct vertices in G. How many simple paths are there from u to v going through w?Graph Theoryhttps://db.gateoverflow.in/299135/virtual-gateThu, 24 Jan 2019 13:12:45 +0000ACE TEST SERIES QUESTION ON Graph Theory
https://db.gateoverflow.in/299120/ace-test-series-question-on-graph-theory
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=4735935059929410075"></p>Graph Theoryhttps://db.gateoverflow.in/299120/ace-test-series-question-on-graph-theoryThu, 24 Jan 2019 12:35:42 +0000SelfDoubt
https://db.gateoverflow.in/297472/selfdoubt
<p><strong>Checking for Euler Path</strong></p>
<p>i.A graph has Euler path if exactly two vertices is of odd degree.</p>
<p>if a graph have euler circuit=>all vertices even degree=>euler circuit which already cover euler path. am i correct? i is necessary and sufficient condition?</p>
<p>So for checking Euler path </p>
<p>we check either</p>
<p>1.Euler Circuit</p>
<p>or </p>
<p>2.Exactly two odd degree then it will have euler path but not euler circuit.</p>
<p>is it correct?</p>
<p> </p>Graph Theoryhttps://db.gateoverflow.in/297472/selfdoubtSun, 20 Jan 2019 15:07:02 +0000MadeEasy Test Series: Discrete Mathematics - Graph Thoery
https://db.gateoverflow.in/297094/madeeasy-test-series-discrete-mathematics-graph-thoery
<p>The number of labelled subgraphs possible for the graph given below.</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=11841882334581494931"></p>Graph Theoryhttps://db.gateoverflow.in/297094/madeeasy-test-series-discrete-mathematics-graph-thoerySat, 19 Jan 2019 17:49:59 +0000Ace Test Series: Graph Theory - Cut Edges
https://db.gateoverflow.in/296709/ace-test-series-graph-theory-cut-edges
If G is a connected simple graph with 10 vertices in which degree of every vertex is 2 then number of cut edges in G is ?Graph Theoryhttps://db.gateoverflow.in/296709/ace-test-series-graph-theory-cut-edgesSat, 19 Jan 2019 05:56:34 +0000made easy adv mock
https://db.gateoverflow.in/296421/made-easy-adv-mock
A graph G is self complementary iff G is isomorphoc to its complement.Let X be a self complementary graph.Which of the following is a viable possibility with regards to connectivity of X and X’ ,where X’ denotes the complement of X?<br />
<br />
a)both X and X’ are disconnected<br />
<br />
b)X is connected and X’ is disconnected<br />
<br />
c)X’ is connected and X’ is disconnected<br />
<br />
d)both X and X’ are connected<br />
<br />
ans is (d) pls explainGraph Theoryhttps://db.gateoverflow.in/296421/made-easy-adv-mockFri, 18 Jan 2019 09:40:48 +0000ME test series question on graph theory
https://db.gateoverflow.in/296030/me-test-series-question-on-graph-theory
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=13808095288188050869"></p>Graph Theoryhttps://db.gateoverflow.in/296030/me-test-series-question-on-graph-theoryThu, 17 Jan 2019 08:43:24 +0000Applied Course 2019 Mock1-36
https://db.gateoverflow.in/295695/applied-course-2019-mock1-36
<p>Naveen invited seven of his friends to a party. At the party, several pairs of people shook hands, although no one shook hands with themselves or shook hands with the same person more than once. After the party, Naveen asked each of his seven friends how many people they shook hands with during the party, and was surprised when they responded with seven distinct positive integers. Given that his friends were truthful, how many hands did Naveen shake?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$4$</li>
<li>$5$</li>
<li>$6$</li>
<li>$7$</li>
</ol>Graph Theoryhttps://db.gateoverflow.in/295695/applied-course-2019-mock1-36Wed, 16 Jan 2019 15:15:06 +0000Seld doubt DM
https://db.gateoverflow.in/295554/seld-doubt-dm
<p>Consider a tree T with n vertices and (<em>n</em> – 1) edges. We define a term called cyclic cardinality of a tree (T) as the number of cycles created when any two vertices of T are joined by an edge. Given a tree with 10 vertices, what is the cyclic cardinality of this tree?</p>Graph Theoryhttps://db.gateoverflow.in/295554/seld-doubt-dmWed, 16 Jan 2019 12:10:46 +0000MadeEasy Subject Test 2019: Graph Thoery - Graph Coloring
https://db.gateoverflow.in/295516/madeeasy-subject-test-2019-graph-thoery-graph-coloring
<p>The number of vertices,edges and colors required for proper coloring in Tripartite graph K<3,2,5> will be :</p>
<ol style="list-style-type:upper-alpha">
<li>10 , 31 , 3</li>
<li>10 , 30 , 3</li>
<li>10 , 30 , 2</li>
<li>None</li>
</ol>Graph Theoryhttps://db.gateoverflow.in/295516/madeeasy-subject-test-2019-graph-thoery-graph-coloringWed, 16 Jan 2019 11:18:52 +0000MadeEasy Full Length Test 2019: Graph Theory - Vertex Connectivity
https://db.gateoverflow.in/295504/madeeasy-full-length-test-graph-theory-vertex-connectivity
<p>The Vertex Connectivity of Graph is :</p>
<p style="text-align:center"><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=16255349216989794686"></p>
<ol style="list-style-type:upper-alpha">
<li>1</li>
<li>2 </li>
<li>3</li>
<li>None</li>
</ol>Graph Theoryhttps://db.gateoverflow.in/295504/madeeasy-full-length-test-graph-theory-vertex-connectivityWed, 16 Jan 2019 11:07:23 +0000Ace Academy Test series
https://db.gateoverflow.in/295415/ace-academy-test-series
If a 2 regular graph G has a perfect matching, then which of the following is NOT true?<br />
<br />
1. G is a cycle graph<br />
<br />
2. Chromatic number of G is 2<br />
<br />
3. Every component of G is even cycle<br />
<br />
4. G is a bipartite graphGraph Theoryhttps://db.gateoverflow.in/295415/ace-academy-test-seriesWed, 16 Jan 2019 07:30:09 +0000How to do such questions.
https://db.gateoverflow.in/295246/how-to-do-such-questions
If $G$ is a bipartite graph with 6 vertices and 9 edges, then the chromatic number of $\overline G$ =Graph Theoryhttps://db.gateoverflow.in/295246/how-to-do-such-questionsTue, 15 Jan 2019 17:33:35 +0000MadeEasy Full Length Test 2018: Graph Theory - Counting
https://db.gateoverflow.in/295122/madeeasy-full-length-test-2018-graph-theory-counting
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=6979421729692082264"></p>
<p>The Number of Labelled possible graph given below ?</p>
<p> </p>
<p>what I did was →</p>
<p>we doesn’t remove any of the edge out of 4 = $\binom{4}{0}$ [Because a Graph is sub-graph of itself]</p>
<p>we can remove any of one edge out of 4 = $\binom{4}{1}$</p>
<p>we can remove any of the two edges out of 4 = $\binom{4}{2}$</p>
<p>similarly , $\binom{4}{3}$ , $\binom{4}{4 }$</p>
<p>then , add of the them</p>
<p> </p>Graph Theoryhttps://db.gateoverflow.in/295122/madeeasy-full-length-test-2018-graph-theory-countingTue, 15 Jan 2019 14:11:29 +0000How this question can be done.
https://db.gateoverflow.in/294924/how-this-question-can-be-done
if G is a bipartite graph with 9 vertices and maximum number of edges, then vertex connectivity of G =Graph Theoryhttps://db.gateoverflow.in/294924/how-this-question-can-be-doneTue, 15 Jan 2019 08:33:55 +0000ME- CBT1
https://db.gateoverflow.in/294525/me-cbt1
<p>Can anyone explain how this is to be solved?</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=7038567099708046092"></p>Graph Theoryhttps://db.gateoverflow.in/294525/me-cbt1Mon, 14 Jan 2019 13:56:41 +0000Made Easy CBT 19 Discrete Maths
https://db.gateoverflow.in/294496/made-easy-cbt-19-discrete-maths
<p>How to solve it(clear explanation please)<img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=12888367405970900147"></p>Graph Theoryhttps://db.gateoverflow.in/294496/made-easy-cbt-19-discrete-mathsMon, 14 Jan 2019 13:31:00 +0000ACE Test series question on Chromatic number
https://db.gateoverflow.in/294274/ace-test-series-question-on-chromatic-number
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=11705626411224168476"></p>Graph Theoryhttps://db.gateoverflow.in/294274/ace-test-series-question-on-chromatic-numberMon, 14 Jan 2019 08:07:38 +0000TRUE/FALSE
https://db.gateoverflow.in/293117/true-false
<p>State TRUE/FALSE</p>
<ol>
<li>Squaring all edges will NOT change the maximum spanning tree</li>
<li>Squaring all edges will NOT change the minimum spanning tree</li>
<li>Squaring all edges will NOT change the second maximum spanning tree</li>
<li>Squaring all edges will NOT change the second minimum spanning tree</li>
<li>Cubing all edges will change the maximum spanning tree</li>
<li>Cubing all edges will change the minimum spanning tree</li>
<li>Cubing all edges will change the second maximum spanning tree</li>
<li>Cubing all edges will change the second minimum spanning tree</li>
</ol>Graph Theoryhttps://db.gateoverflow.in/293117/true-falseFri, 11 Jan 2019 15:49:40 +0000Virtual Gate Test Series: Discrete Mathematics - Graph Theory
https://db.gateoverflow.in/291697/virtual-gate-test-series-discrete-mathematics-graph-theory
<p>Let $G$ be a graph on $n$ vertices with $4n-16$ edges.Consider the following:
<br>
1. There is a vertex of degree smaller than $8$ in $G.$
<br>
<br>
2. There is a vertex such that there are less than $16$ vertices at a distance exactly $2$ from it.
<br>
<br>
Which of the following is TRUE:</p>
<ol start="1" style="list-style-type:lower-alpha">
<li> 1 only</li>
<li>2 only</li>
<li> Both 1 and 2</li>
<li> Neither 1 nor 2</li>
</ol>Graph Theoryhttps://db.gateoverflow.in/291697/virtual-gate-test-series-discrete-mathematics-graph-theoryTue, 08 Jan 2019 20:30:43 +0000Graph_Self Doubt
https://db.gateoverflow.in/291228/graph_self-doubt
Let G be a simple graph with 11 vertices . if degree of each vertex is atleast 3 and atmost 5 , then the number of edges in G should lie between<br />
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I got 16 and 28Graph Theoryhttps://db.gateoverflow.in/291228/graph_self-doubtTue, 08 Jan 2019 09:40:25 +0000rc test
https://db.gateoverflow.in/291133/rc-test
Let G be a graph with 100 vertices numbered from 1 to 100. Two vertices i and j are adjacent if $\left | i-j \right |=8 $ or $\left | i-j \right |=12$<br />
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the number of connected components in G are<br />
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a)8<br />
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b)4<br />
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c)12<br />
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d)25Graph Theoryhttps://db.gateoverflow.in/291133/rc-testTue, 08 Jan 2019 06:38:15 +0000rc test series
https://db.gateoverflow.in/291126/rc-test-series
Assume G is a connected planar graph that has 12 vertices and 17 regions.all interior regions are bounded by a cycle of length 3(ie 3 edge).find the number of edges bounding the interior region?Graph Theoryhttps://db.gateoverflow.in/291126/rc-test-seriesTue, 08 Jan 2019 06:18:24 +0000rc test series
https://db.gateoverflow.in/291120/rc-test-series
<p><a tabindex="0">consider a simple graph G with k components.If each component has n1,n2,.....nk vertices,<strong><em>then</em></strong> the <strong><em>maximum</em></strong> number of edges in G is</a></p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=10762486716550401009"></p>Graph Theoryhttps://db.gateoverflow.in/291120/rc-test-seriesTue, 08 Jan 2019 05:51:07 +0000