GATE Overflow - Recent questions in Graph Theory
http://gateoverflow.in/questions/mathematics/discrete-mathematics/graph-theory
Powered by Question2AnswerGATE2017-2-23
http://gateoverflow.in/118594/gate2017-2-23
$G$ 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 _________ .Graph Theoryhttp://gateoverflow.in/118594/gate2017-2-23Tue, 14 Feb 2017 10:05:53 +0000gatebook mock 2
http://gateoverflow.in/117278/gatebook-mock-2
Consider the collection of all un directed graphs with 10 nodes and 6 edges. Let M and m, respectively, be the maximum and minimum number of connected components in any graph in the collection. If a graph has no self loops and there is at most one edge between any pair of nodes, which of the following is true?<br />
<br />
(A) M = 10, m = 10<br />
<br />
(B) M = 10, m = 1<br />
<br />
(C) M = 7, m = 4<br />
<br />
(D) M = 6, m = 4<br />
<br />
<br />
<br />
Shouldn't the answer be D?Graph Theoryhttp://gateoverflow.in/117278/gatebook-mock-2Wed, 08 Feb 2017 07:05:02 +0000Virtual Test Series
http://gateoverflow.in/116988/virtual-test-series
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=846771792498572003"></p>Graph Theoryhttp://gateoverflow.in/116988/virtual-test-seriesTue, 07 Feb 2017 12:15:16 +0000Bipartite Graph
http://gateoverflow.in/116936/bipartite-graph
If G is a bipartite planar graph with n vertices, then what is the maximum number of egdes in G.<br />
<br />
a) 2n-4<br />
<br />
b) 3n-2<br />
<br />
c) n-2<br />
<br />
d) nGraph Theoryhttp://gateoverflow.in/116936/bipartite-graphTue, 07 Feb 2017 10:49:53 +0000Graph Theory (Chromatic no)
http://gateoverflow.in/116685/graph-theory-chromatic-no
<p><img alt="" height="116" src="http://gateoverflow.in/?qa=blob&qa_blobid=12318005620946289803" width="679"></p>Graph Theoryhttp://gateoverflow.in/116685/graph-theory-chromatic-noMon, 06 Feb 2017 21:02:55 +0000ace mock test
http://gateoverflow.in/116443/ace-mock-test
<p>Is this solution wrong?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8105753181938441135"></p>Graph Theoryhttp://gateoverflow.in/116443/ace-mock-testMon, 06 Feb 2017 08:18:06 +0000Dirac Theorem
http://gateoverflow.in/114934/dirac-theorem
If d(V) ≥ n/2 for each vertex V in G, then G is hamiltonian. [d(V) is the degree of a vertex V]<br />
<br />
True/False explain:Graph Theoryhttp://gateoverflow.in/114934/dirac-theoremThu, 02 Feb 2017 14:01:37 +0000Euler Path
http://gateoverflow.in/114086/euler-path
<p><em><strong>Which of the following Graph has Euler Path but is not an Euler Graph?
<br>
A. K<sub>1,1 </sub>
<br>
B.K<sub>2,10 </sub>
<br>
C.K<sub>2,11</sub>
<br>
D.K<sub>10,11.</sub></strong></em></p>Graph Theoryhttp://gateoverflow.in/114086/euler-pathTue, 31 Jan 2017 17:16:17 +0000graph theory
http://gateoverflow.in/113599/graph-theory
<p>How many distinct paths of length 4 that do not visit the same node more than once are there between node 0 and node 1?
<br>
<img alt="image:EM3/Q2a.PNG" height="143" src="http://gatexcel.co.in/cache/EM3/Q2a.PNG" width="151"></p>Graph Theoryhttp://gateoverflow.in/113599/graph-theoryMon, 30 Jan 2017 18:33:27 +0000Graph Theory : Simple Path in Simple Graph
http://gateoverflow.in/113565/graph-theory-simple-path-in-simple-graph
What should be the maximum lenght of path consisting of n veritces ?<br />
<br />
Is, it should be n or n-1.Graph Theoryhttp://gateoverflow.in/113565/graph-theory-simple-path-in-simple-graphMon, 30 Jan 2017 16:42:53 +0000euler and ham cycle
http://gateoverflow.in/112618/euler-and-ham-cycle
<p>Which of the following statements is true?</p>
<ul>
<li><img alt="" src="https://s3-ap-southeast-1.amazonaws.com/gw-mdsy/student/images/wright.gif">Every complete graph contain Hamiltonian cycle</li>
<li>Every complete graph contain Euler cycle</li>
<li>Both (a) and (b)</li>
<li><img alt="" src="https://s3-ap-southeast-1.amazonaws.com/gw-mdsy/student/images/wrong.gif">None of the above</li>
</ul>
<p>It should be none of the above because when no. of vertices are 2 it doesnt follow these conditions </p>Graph Theoryhttp://gateoverflow.in/112618/euler-and-ham-cycleSat, 28 Jan 2017 16:29:14 +0000G be a simple graph on 8 vertices such that there is a vertices of degrees 1,2,3,4,5,6,7 respectively - then
http://gateoverflow.in/112057/simple-graph-vertices-there-vertices-degrees-respectively
Which of the following can be the degree of the last vertex?<br />
<br />
(A) 3<br />
<br />
(B) 0<br />
<br />
(C) 5<br />
<br />
(D) 4Graph Theoryhttp://gateoverflow.in/112057/simple-graph-vertices-there-vertices-degrees-respectivelyFri, 27 Jan 2017 16:31:57 +0000Graph Theroy
http://gateoverflow.in/111612/graph-theroy
<p><img alt="" height="447" src="https://i.stack.imgur.com/qaID3.png" width="527"></p>
<p>Does this graph contains cycle????</p>
<p><a rel="nofollow" href="http://math.stackexchange.com/questions/1490053/what-is-the-difference-between-a-loop-cycle-and-strongly-connected-components-i">http://math.stackexchange.com/questions/1490053/what-is-the-difference-between-a-loop-cycle-and-strongly-connected-components-i</a></p>Graph Theoryhttp://gateoverflow.in/111612/graph-theroyThu, 26 Jan 2017 13:04:28 +0000Virtual Gate [Graph]
http://gateoverflow.in/110367/virtual-gate-graph
<p><em>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?</em></p>Graph Theoryhttp://gateoverflow.in/110367/virtual-gate-graphTue, 24 Jan 2017 09:00:19 +0000Virtual GATe
http://gateoverflow.in/109856/virtual-gate
<p>If both x and y are integers, then the point P(x,y) is called a lattice point of the plane. Suppose P<sub>i</sub>, 1 <= i <= 5, are five (different) lattice points. We form a complete graph using these 5 points and the unique straight line segments (edges) determined by the C(5,2) = 10 pairs of these points. For any given values of lattice points, the minimum number of edges which will have its midpoint (of the line segment corresponding to that edge) as a lattice point is:</p>
<p>(A) 1
<br>
(B) 2
<br>
(C) 3
<br>
(D) 4</p>
<p> </p>
<p>Explain what they are asking and then solution.I am not able to understand question also</p>Graph Theoryhttp://gateoverflow.in/109856/virtual-gateMon, 23 Jan 2017 14:23:55 +0000Graph_Theory
http://gateoverflow.in/108420/graph_theory
A graph has a degree sequence <1,1,2,2,3,3,3,3> the number of edges in the graph?<br />
<br />
a) 18 b)9 c)36 d)8Graph Theoryhttp://gateoverflow.in/108420/graph_theoryFri, 20 Jan 2017 15:37:57 +0000no. of edges
http://gateoverflow.in/108399/no-of-edges
A graph G has k isolated vertices and n + k vertices. The maximum number of edges graph G can have?<br />
<br />
a) n(n-1) b)n(n-1)/2) c) n(n-k+1)/2 d) n(n+k-1)/2Graph Theoryhttp://gateoverflow.in/108399/no-of-edgesFri, 20 Jan 2017 15:10:35 +0000Graphs
http://gateoverflow.in/108398/graphs
A sequence d = is graphic if there is a simple non-directed graph with degree sequence d then which one of the following sequences is graphic?<br />
<br />
a) (2, 3, 3, 4, 4, 5) b) (1, 3, 3, 3) c) (2, 3, 3, 4, 5, 6, 7) d) (2, 3, 3, 3, 3)Graph Theoryhttp://gateoverflow.in/108398/graphsFri, 20 Jan 2017 15:06:18 +0000Graph
http://gateoverflow.in/108395/graph
1. Suppose that G is a non-directed graph with 12 edges. Suppose that G has 6 vertices of degree 3 and the rest have degrees less than 3. The minimum number of vertices G can have?<br />
<br />
a) 2 b) 0 c)1 d)3<br />
<br />
I am getting 3..plz verifyGraph Theoryhttp://gateoverflow.in/108395/graphFri, 20 Jan 2017 15:03:54 +0000Graph Theory Problem-Test Series
http://gateoverflow.in/108391/graph-theory-problem-test-series
A Connected Graph has Cut edge, Then Graph has Cut vertex also.<br />
<br />
1. True<br />
<br />
2. False<br />
<br />
Choose Correct One.Graph Theoryhttp://gateoverflow.in/108391/graph-theory-problem-test-seriesFri, 20 Jan 2017 14:59:48 +0000GRAPH_degree seq
http://gateoverflow.in/108382/graph_degree-seq
Is there any simple graph with degree sequence<br />
<br />
<1,1,1,1,2,2,3,3,3,3>Graph Theoryhttp://gateoverflow.in/108382/graph_degree-seqFri, 20 Jan 2017 14:40:54 +0000When they don't mention type of tree then if it's mandatory to take 'Binary Tree'(Check Description)
http://gateoverflow.in/107483/when-mention-mandatory-take-binary-tree-check-description
<p><span class="marker">The minimum number of vertices having degree 1 in a tree of at least 10 vertices is ______________.</span></p>
<p>If we consider this question, then first answer comes in our mind is '2', right?</p>
<p>But what if Tree isn't binary?</p>
<p> if root node has 9 leaf nodes, so all those nodes having degree 1, right? So answer could be:<strong>9</strong></p>Graph Theoryhttp://gateoverflow.in/107483/when-mention-mandatory-take-binary-tree-check-descriptionWed, 18 Jan 2017 12:52:13 +0000Graph Theory
http://gateoverflow.in/107480/graph-theory
Let G be a undirected graph with 35 edges and degree of each vertex is at least 3 then maximum number of vertices possible in G is<br />
<br />
(A) 22<br />
(B) 23<br />
(C) 24<br />
(D) 25<br />
<br />
P.S. Explain with ease, if possible!Graph Theoryhttp://gateoverflow.in/107480/graph-theoryWed, 18 Jan 2017 12:45:46 +0000Graph Theory
http://gateoverflow.in/107221/graph-theory
How to learn and understand graph theory in 23 days i mean before gate exam? Can anybody help in this.Like there are many new terms bipartite graph etc etc i m not able to learn some complicated names ?<br />
<br />
Any video lectures or anything please help :)Graph Theoryhttp://gateoverflow.in/107221/graph-theoryTue, 17 Jan 2017 21:06:55 +0000MADE EASY TEST SERIES
http://gateoverflow.in/106729/made-easy-test-series
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8856951113969376819"></p>Graph Theoryhttp://gateoverflow.in/106729/made-easy-test-seriesTue, 17 Jan 2017 07:01:48 +0000What is the expected length of the cycle containing vertex 1?
http://gateoverflow.in/106462/what-is-the-expected-length-of-the-cycle-containing-vertex-1
<p>A random permutation π of set[n] = {1, 2, …, n} can be represent by a directed graph on n vertices with directed arc (i, π<sub>i</sub>) where π<sub>i</sub> is the i<sup>th</sup> entry in the permutation. Observe that the resulting graph is just a collection of disjoint cycles.
<br>
What is the expected length of the cycle containing vertex 1?</p>
<ol>
<li> n(n-1)/2n</li>
<li> (n+1)/2n</li>
<li> ((n-1))/2</li>
<li> ((n+1))/2</li>
</ol>
<p> </p>
<p>/pls explain the question </p>Graph Theoryhttp://gateoverflow.in/106462/what-is-the-expected-length-of-the-cycle-containing-vertex-1Mon, 16 Jan 2017 13:54:25 +0000Testbook
http://gateoverflow.in/106414/testbook
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9826512353065079146"></p>Graph Theoryhttp://gateoverflow.in/106414/testbookMon, 16 Jan 2017 12:30:45 +0000Non-isomorphic graphs
http://gateoverflow.in/105987/non-isomorphic-graphs
<p>How many <em><strong>non-isomorphic</strong></em> simple graph are there with <strong>N</strong> vertices, where <strong>N = 4 ?</strong></p>Graph Theoryhttp://gateoverflow.in/105987/non-isomorphic-graphsSun, 15 Jan 2017 15:37:27 +0000#nlc payment
http://gateoverflow.in/105975/%23nlc-payment
@ arjun sir for nlc application i have done sbi collect payment 2 days before but still nlc is showing fee paid status as not paid what to do nowGraph Theoryhttp://gateoverflow.in/105975/%23nlc-paymentSun, 15 Jan 2017 15:27:44 +0000Number of Sums
http://gateoverflow.in/105861/number-of-sums
<table style="width:100%">
</table>
<table style="width:100%">
<tbody>
<tr>
<td> </td>
<td>The function for finding the fibonacci series is given as follows :
<br>
<br>
<img alt="Image not present" src="http://s3-ap-southeast-1.amazonaws.com/gate-content-images/data/images/common/papers/partners/34/580/image033.png">
<br>
<br>
The number of additions taken in evaluating fib(5) is.</td>
</tr>
</tbody>
</table>
<p>Your Answer:
<br>
<br>
4
<br>
<br>
Correct Answer: 7 Status: incorrect</p>Graph Theoryhttp://gateoverflow.in/105861/number-of-sumsSun, 15 Jan 2017 11:51:57 +0000Which is maximum Planar graph whose Line Graph is Planar?(Check the answer)
http://gateoverflow.in/105345/which-maximum-planar-graph-whose-graph-planar-check-answer
Graph Theoryhttp://gateoverflow.in/105345/which-maximum-planar-graph-whose-graph-planar-check-answerSat, 14 Jan 2017 06:26:19 +0000How many maximum cycles possible in any Complete graph? (Unlabelled nodes)
http://gateoverflow.in/105343/many-maximum-cycles-possible-complete-graph-unlabelled-nodes
Graph Theoryhttp://gateoverflow.in/105343/many-maximum-cycles-possible-complete-graph-unlabelled-nodesSat, 14 Jan 2017 06:20:45 +0000#Chromatic number , Planarity
http://gateoverflow.in/104130/%23chromatic-number-planarity
Let G be a planar graph such that every face is bordered by exactly 3 edges.Which of the following can never be the value for χ(G) ? (where χ(G) is the chromatic number of G)<br />
<br />
a) 2<br />
<br />
b) 3<br />
<br />
c) 4<br />
<br />
d) None of these<br />
<br />
PS : (Explain: "every face is bordered by exactly 3 edges. ")Graph Theoryhttp://gateoverflow.in/104130/%23chromatic-number-planarityWed, 11 Jan 2017 15:09:19 +0000Test Book Test
http://gateoverflow.in/103993/test-book-test
An Undirected graph G with only one simple path between each pair of vertices has two vertices of degree 4, one vertex of degree 3 and two vertices of degree 2. Number of vertices of degree 1 are _____________ ?Graph Theoryhttp://gateoverflow.in/103993/test-book-testWed, 11 Jan 2017 09:55:37 +0000Graph
http://gateoverflow.in/103064/graph
<p style="text-align:center"><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=112934128026092186"></p>Graph Theoryhttp://gateoverflow.in/103064/graphMon, 09 Jan 2017 11:08:49 +0000if graph is loop free then how can it have cycle
http://gateoverflow.in/101745/if-graph-is-loop-free-then-how-can-it-have-cycle
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=17020158051302376799"></p>Graph Theoryhttp://gateoverflow.in/101745/if-graph-is-loop-free-then-how-can-it-have-cycleFri, 06 Jan 2017 17:22:05 +0000graph
http://gateoverflow.in/101041/graph
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.Graph Theoryhttp://gateoverflow.in/101041/graphThu, 05 Jan 2017 11:13:58 +0000graph theory
http://gateoverflow.in/100206/graph-theory
Assumed undirected graph G is connected. G has 6vertices and 10 edges. Find<br />
the minimum number of edges whose deletion from graph G is always guarantee<br />
that it will become disconnected.Graph Theoryhttp://gateoverflow.in/100206/graph-theoryTue, 03 Jan 2017 20:57:09 +0000handshake lemma
http://gateoverflow.in/100080/handshake-lemma
<p>every vertex has a minimum degree, therefore, least number of edges that will be in the graph is given by the handshaking lemma as = <em>m</em><em>i</em><em>n</em>×|<em>v</em>|/2=2 E is right?</p>
<p> </p>
<p> </p>Graph Theoryhttp://gateoverflow.in/100080/handshake-lemmaTue, 03 Jan 2017 14:33:26 +0000Maths: Graph Theory
http://gateoverflow.in/99639/maths-graph-theory
<p>Let G be a graph with 10 vertices and 31 edges. If G has 3 vertices of degree 10, 1 vertex of degree 8 and 2 vertices of degree 5 and the other four vertices of degree at least 3, how many vertices are of degree 3________?</p>
<p>my solution:
<br>
<br>
Σ deg(v) = 2|E|</p>
<p>3*10 + 1*8 + 2*5 + 4*(>=3) = 2*31
<br>
<br>
4*(>=3) = 62- (30+8+10) = 14
<br>
<br>
I think we can have 3 vertices each of degree 3 and vertex of degree 5, so my answer is 3 but given answer is 2.
<br>
<br>
<span class="marker">Given answer: 2</span></p>Graph Theoryhttp://gateoverflow.in/99639/maths-graph-theoryMon, 02 Jan 2017 16:12:18 +0000Maths: Functions
http://gateoverflow.in/99351/maths-functions
<p>if $f(x)=\frac{x-1}{x+1}$ , x∈R-{-1}, then f<sup>-1</sup>(x) is equal to</p>
<p> </p>
<p>$a. \frac{x-1}{x+1} b.\frac{x+1}{x-1} c.\frac{2}{1+x}$ d.Does Not exist</p>Graph Theoryhttp://gateoverflow.in/99351/maths-functionsMon, 02 Jan 2017 05:41:33 +0000How this statement is true
http://gateoverflow.in/99316/how-this-statement-is-true
How this is true ?<br />
<br />
$_{r}^{\frac{n(n-1)}{2}}\textrm{C} = 2^{\frac{n(n-1))}{2}}$Graph Theoryhttp://gateoverflow.in/99316/how-this-statement-is-trueMon, 02 Jan 2017 04:12:10 +0000MATCHING NUMBER
http://gateoverflow.in/98836/matching-number
what is the matching number of $K_{2,3}$ graph.and also explain matching number of $K_{m,n}$(simplification).Graph Theoryhttp://gateoverflow.in/98836/matching-numberSat, 31 Dec 2016 09:58:55 +0000A graph $G$ is Eulerian path iff degree of each vertex is even with atmost one trivial component
http://gateoverflow.in/98763/graph-eulerian-degree-vertex-with-atmost-trivial-component
<p>For this proof ,proving</p>
<p>$\Rightarrow$ If Graph $G$ is eulerian then degree of each vertex is even with atmost one trivial component.</p>
<p>As $G$ is Eulerian ,it means it **must not** repeat Edges but can repeat vertices.Now for the Eulerian (path) traversal ,we pass through that vertex using two incident edges,one for entry and other for exit.</p>
<p> </p>
<p> </p>
<p>Then what is wrong in this graph?</p>
<p> </p>
<p><img alt="" height="174" src="http://gateoverflow.in/?qa=blob&qa_blobid=9141544755438812825" width="468"></p>
<p> </p>
<p>Here we have Eulerian path traversal as</p>
<p>
<br>
$C\rightarrow A \rightarrow B \rightarrow D \rightarrow C \rightarrow F \rightarrow E \rightarrow H \rightarrow G \rightarrow F $</p>
<p>but here degree of $C,F =3$ contradictory....</p>
<p>
<br>
help me out where i am wrong</p>
<p> </p>Graph Theoryhttp://gateoverflow.in/98763/graph-eulerian-degree-vertex-with-atmost-trivial-componentSat, 31 Dec 2016 07:28:13 +0000graph theory
http://gateoverflow.in/97768/graph-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11696266218365235197"></p>Graph Theoryhttp://gateoverflow.in/97768/graph-theoryWed, 28 Dec 2016 13:48:36 +0000[Rosen Textbook Problem] Complementary Graph
http://gateoverflow.in/97560/rosen-textbook-problem-complementary-graph
The complementary graph G' of a simple graph G has the same vertices as G. Two vertices are adjacent in G' if and only if they are not adjacent in G. Define Qn' (Hypercube complement).<br />
<br />
Answer given :-The graph whose vertices are bit strings of length n and two vertices are adjacent if the bit string represented by them differe by more than one bit.<br />
<br />
I want to understand that whether the complement graph will have self loops?Because the answer given doesn't consider self loops.I mean why are we not considering the bit strings that are differing by 0 bit,as these are also not there in original graph ,so it must be in complementary graph?Graph Theoryhttp://gateoverflow.in/97560/rosen-textbook-problem-complementary-graphTue, 27 Dec 2016 23:53:29 +0000planar region
http://gateoverflow.in/96892/planar-region
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7262737156748786251"></p>
<p> </p>
<ul>
<li>How many planar regions?</li>
<li>How many closed regions? and how many are unbounded?</li>
<li>How many of then are bounded by a cycle of length $4$ ?</li>
<li>Now, for example (a different question, not related to above diagram ) a question says, In a connected 3 regular graph, every planar region is bounded by exactly 5 edges, then count no of edges?</li>
</ul>
<p>Please explain the last QS with the help of Euler's equation. </p>Graph Theoryhttp://gateoverflow.in/96892/planar-regionMon, 26 Dec 2016 09:18:35 +0000connectivity
http://gateoverflow.in/96717/connectivity
<p>Consider a simple connected undirected graph <em>G</em> which has m vertices and n edges. Which of the following condition always guarantee that after removal of those number of edges graph will be disconnected?</p>
<p><em>a)m</em> – <em>n</em> + 2</p>
<p>b)$_{2}^{m}\textrm{C}-n+2$</p>
<p> <em>c)n</em> – 2</p>
<p>d)None of the above</p>Graph Theoryhttp://gateoverflow.in/96717/connectivityMon, 26 Dec 2016 02:11:12 +0000E = 2N -3
http://gateoverflow.in/96274/e-2n-3
<p>I read in <a rel="nofollow" href="http://gateoverflow.in/28955/given-vertex-edges-how-find-non-isomorphic-graphs-possible">http://gateoverflow.in/28955/given-vertex-edges-how-find-non-isomorphic-graphs-possible</a> question explanantion,it was written that e=2n-3 where e= number of edges and n is no of vertices.</p>
<p>how is it derived??can anyone tell me the source??</p>Graph Theoryhttp://gateoverflow.in/96274/e-2n-3Sat, 24 Dec 2016 15:57:38 +0000maths
http://gateoverflow.in/96149/maths
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6880132629596798735"></p>Graph Theoryhttp://gateoverflow.in/96149/mathsSat, 24 Dec 2016 09:52:05 +0000