GATE Overflow - Recent questions tagged graph-theory
http://gateoverflow.in/tag/graph-theory
Powered by Question2Answer#Graphtheory
http://gateoverflow.in/130285/%23graphtheory
Construct a graph G with edge connectivity of G =4 ,vertex connectivity of G =3 and degree of every vertex of G >=5Graph Theoryhttp://gateoverflow.in/130285/%23graphtheorySun, 21 May 2017 02:56:10 +00002 - connected graph
http://gateoverflow.in/130141/2-connected-graph
<p>For a <strong>regular graph</strong> how much large the value of degree (for each vertices) should be such that the graph is $2$ - connected. (vertex wise).</p>
<p>I did in this way :</p>
<p>$\begin{align*} &\quad \kappa(G) \leq \frac{2\cdot e}{n} \qquad \text{ where } \kappa(G) = \text{ vertex connectivity } \\ &\Rightarrow 2 \leq \frac{2\cdot e}{n} \\ &\Rightarrow n \leq e \\ &\Rightarrow n \leq \frac{\sum \left ( d_i \right )}{2} \\ &\Rightarrow n \leq \frac{n \cdot d}{2} \\ &\Rightarrow d \geq 2 \\ \end{align*}$</p>
<p>The above case can be realized by thinking of a <strong>cycle graph</strong> of $n$ vertices.</p>
<p>But in the following case :</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=15360590681287688332"></p>
<p>This graph is 3 regular and not 2- connected although $d \geq 2$ is satisfied.</p>
<p>Why this $d \geq 2$ is trivial and not working in some cases ?</p>Graph Theoryhttp://gateoverflow.in/130141/2-connected-graphFri, 19 May 2017 07:12:05 +0000GATE Graph Theory
http://gateoverflow.in/129447/gate-graph-theory
Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?<br />
<br />
( A ) G1 = (V, E1) where E1 = {(u, v) | (u, v) ∉ E}<br />
( B ) G2 = (V, E2) where E2 = {(u, v) | (v, u) ∉ E}<br />
( C ) G3 = (V, E3) where E3 = {(u, v) | there ish a path of length ≤ 2 from u to v in E}<br />
( D ) G4 = (V4, E) where V4 is the set of vertices in G which are not isolated<br />
<br />
Can anyone give a detailed answer to this question, please? :)Graph Theoryhttp://gateoverflow.in/129447/gate-graph-theoryFri, 12 May 2017 19:24:26 +0000Graph Theory
http://gateoverflow.in/129355/graph-theory
algorithm to find more than one path between any two vertices of a graph G=(V,E) , with a complexity of O(VE) ?Graph Theoryhttp://gateoverflow.in/129355/graph-theoryFri, 12 May 2017 08:04:59 +0000Graph theory and Applications Bondy and Murty Exercise Qn 1.9
http://gateoverflow.in/129036/graph-theory-and-applications-bondy-and-murty-exercise-qn-1
<p>A k partite graph is one where vertex set can be partitioned into k subsets so that no edge has both end in any one subset.</p>
<p>A complete k partite graph is one that is simple and in which each vertex is joined to every other vertex that is not in the same subset. The complete m-partite graph on n vertices in which each part has either floor(n/m) or ceil(n/m) vertices is denoted by T<sub>m,n</sub> . Show that</p>
<p>a) | E(T<sub>m,n</sub>) | = $\binom{n-k}{2} + (m-1)\binom{k+1}{2} , k = \left \lfloor n/m \right \rfloor$</p>
<p>b) If G is a complete m-partite graph on n vertices then | E(G) | <= | E(T<sub>m,n</sub>)|, with equality only if G isomorphic to T<sub>m,n</sub></p>Graph Theoryhttp://gateoverflow.in/129036/graph-theory-and-applications-bondy-and-murty-exercise-qn-1Tue, 09 May 2017 16:09:49 +0000keneth r rosen
http://gateoverflow.in/128471/keneth-r-rosen
how to prove that sum of all the vertices in a graph G is equal to twice the number of edges in G.<br />
<br />
please explain step by step .Graph Theoryhttp://gateoverflow.in/128471/keneth-r-rosenSun, 07 May 2017 13:28:40 +0000Relation between k and k-1 edge connected graph
http://gateoverflow.in/128029/relation-between-k-and-k-1-edge-connected-graph
Is every k connected graph is k-1 connected or the reverse? I always get confused. Can someone explain with the help of an example.Algorithmshttp://gateoverflow.in/128029/relation-between-k-and-k-1-edge-connected-graphWed, 03 May 2017 23:36:19 +0000PGEE 2017
http://gateoverflow.in/127521/pgee-2017
Consider a graph where vertex having number 2 to 12 (including 2 and 12), there is an edge between two vertex x and y iff x divides y<br />
<br />
What would be maximum path length between any two vertices of graph ?Graph Theoryhttp://gateoverflow.in/127521/pgee-2017Sun, 30 Apr 2017 18:04:30 +0000PGEE 2017
http://gateoverflow.in/127520/pgee-2017
Consider a graph where vertex having number 2 to 12 (including 2 and 12), there is an edge between two vertex x and y iff x divides<br />
<br />
Which vertex will have highest in degree ?Graph Theoryhttp://gateoverflow.in/127520/pgee-2017Sun, 30 Apr 2017 18:00:23 +0000PGEE 2017
http://gateoverflow.in/127519/pgee-2017
Consider a graph where vertex having number 2 to 12 (including 2 and 12), there is an edge between two vertex x and y iff x divides y<br />
<br />
Find number of strongly connected componentsGraph Theoryhttp://gateoverflow.in/127519/pgee-2017Sun, 30 Apr 2017 17:58:18 +0000Self-Doubt
http://gateoverflow.in/126868/self-doubt
Every Planar graph have vertex cover of size atmost 3n/4.<br />
<br />
Can someone provide a good link to understand the above fact?<br />
<br />
Or a good explanation is most welcome.Graph Theoryhttp://gateoverflow.in/126868/self-doubtTue, 25 Apr 2017 06:41:09 +0000graph theory
http://gateoverflow.in/124669/graph-theory
A graph consists of only one vertex,which is isolated ..Is that graph<br />
<br />
A) a complete graph ???<br />
<br />
B) a clique???<br />
<br />
C) connected graph ???<br />
<br />
Please explain your answer ...Graph Theoryhttp://gateoverflow.in/124669/graph-theoryFri, 07 Apr 2017 17:38:26 +0000ISI Entrance Exam MTech (CS)
http://gateoverflow.in/124367/isi-entrance-exam-mtech-cs
Consider all possible trees with n nodes. Let k be the number<br />
of nodes with degree greater than 1 in a given tree. What is<br />
the maximum possible value of k?Graph Theoryhttp://gateoverflow.in/124367/isi-entrance-exam-mtech-csThu, 06 Apr 2017 00:52:41 +0000Graph Theory
http://gateoverflow.in/123618/graph-theory
let G=(V,E) be an connected graph, let $\left | V \right |= n$<br />
<br />
Find largest value of n such that<br />
<br />
i) G is complete &<br />
<br />
ii) G is bipartite<br />
<br />
with valid proofAlgorithmshttp://gateoverflow.in/123618/graph-theorySun, 02 Apr 2017 22:12:23 +0000Graph Theory Path
http://gateoverflow.in/123440/graph-theory-path
What is the difference between path and Euler path?Graph Theoryhttp://gateoverflow.in/123440/graph-theory-pathSun, 02 Apr 2017 02:20:33 +0000No of spanning Trees
http://gateoverflow.in/122066/no-of-spanning-trees
Let $K_n$ denote the complete undirected graph with $n$ vertices where n is an even number. Find the maximum number of spanning trees of $K_n$ that can be formed in such a way that no two of these spanning trees have a common edge.Graph Theoryhttp://gateoverflow.in/122066/no-of-spanning-treesSun, 19 Mar 2017 13:10:09 +0000graph theory
http://gateoverflow.in/121379/graph-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14124213158983667542"></p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5624474628795835148"></p>Graph Theoryhttp://gateoverflow.in/121379/graph-theorySun, 12 Mar 2017 17:52:08 +0000graph theory
http://gateoverflow.in/121304/graph-theory
<p><strong>chromatic number of a graph <= ( maxdegree of the graph ) + 1 </strong></p>
<p>can somebody explain how ?</p>Graph Theoryhttp://gateoverflow.in/121304/graph-theorySat, 11 Mar 2017 16:53:30 +0000graph theory
http://gateoverflow.in/121303/graph-theory
A graph with n vertices and 0 edges.can this graph be called as Bipartite ? i mean can we simply partition the n vertices into two sets of vertices such that there is no edge within the set as well there is no edge between the two sets and say it as a Bipartite graph ?Graph Theoryhttp://gateoverflow.in/121303/graph-theorySat, 11 Mar 2017 16:50:02 +0000graph theory
http://gateoverflow.in/121282/graph-theory
State TRUE or FALSE.<br />
<br />
The chromatic number of a Bi-partite graph is ALWAYS 2.Graph Theoryhttp://gateoverflow.in/121282/graph-theorySat, 11 Mar 2017 10:57:10 +0000graph theory
http://gateoverflow.in/121278/graph-theory
The cardinality of the vertex-cut ( seperating set ) of a complete graph with n vertices is ___Graph Theoryhttp://gateoverflow.in/121278/graph-theorySat, 11 Mar 2017 10:16:37 +0000graph theory
http://gateoverflow.in/121240/graph-theory
In a Bipartite graph,the size of the maximum matching is equal to the size of the minimum vertex cover ...can somebody prove this logically ?Graph Theoryhttp://gateoverflow.in/121240/graph-theoryFri, 10 Mar 2017 19:06:22 +0000graph theory
http://gateoverflow.in/121147/graph-theory
<p>The number of <strong>independent sets</strong> in a complete graph with n vertices is ____</p>Graph Theoryhttp://gateoverflow.in/121147/graph-theoryFri, 10 Mar 2017 10:03:49 +0000graph theory
http://gateoverflow.in/121111/graph-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=16494923851889305305"></p>
<p>can somebody explain the logic behind this theorem ?</p>Graph Theoryhttp://gateoverflow.in/121111/graph-theoryThu, 09 Mar 2017 21:25:28 +0000graph theory
http://gateoverflow.in/121050/graph-theory
<p> </p>
<p>Find </p>
<p>1) Vertex connectivity </p>
<p>2) Edge connectivity </p>
<p>3) Is it a seperable graph ? If so then find the cut-vertex </p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11584695799903342456"></p>Graph Theoryhttp://gateoverflow.in/121050/graph-theoryThu, 09 Mar 2017 10:25:56 +0000graph theory
http://gateoverflow.in/121042/graph-theory
<p> Find </p>
<p>1) Vertex connectivity </p>
<p>2) Edge connectivity </p>
<p>3) Is it a seperable graph ? If so then find the cut-vertex </p>
<p>4) Is {v<sub>1</sub>,v<sub>2</sub>,v<sub>5</sub>} a cut-set ?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=38764623861261551"></p>Graph Theoryhttp://gateoverflow.in/121042/graph-theoryThu, 09 Mar 2017 10:10:12 +0000graph theory
http://gateoverflow.in/120989/graph-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13344674821615170849"></p>Graph Theoryhttp://gateoverflow.in/120989/graph-theoryWed, 08 Mar 2017 20:35:19 +0000graph theory
http://gateoverflow.in/120988/graph-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=16810418372386685647"></p>Graph Theoryhttp://gateoverflow.in/120988/graph-theoryWed, 08 Mar 2017 20:31:38 +0000graph theory
http://gateoverflow.in/120984/graph-theory
<p> </p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9619004610669890152"></p>Graph Theoryhttp://gateoverflow.in/120984/graph-theoryWed, 08 Mar 2017 20:22:47 +0000ISI 2015 PCB C3
http://gateoverflow.in/120885/isi-2015-pcb-c3
For a positive integer n, let G = (V, E) be a graph, where V = {0,1}^n, i.e., V is the set of vertices has one to one correspondence with the set of all n-bit binary strings and E = {(u,v) | u, v belongs to V, u and v differ in exactly one bit position}.<br />
<br />
i) Determine size of E<br />
<br />
ii) Show that G is connectedGraph Theoryhttp://gateoverflow.in/120885/isi-2015-pcb-c3Wed, 08 Mar 2017 07:22:42 +0000ISI 2016 PCB C8
http://gateoverflow.in/120576/isi-2016-pcb-c8
Consider $2n$ committees, each having at least $2n$ persons, formed from a group of $4n$ persons. Prove that there exists at least one person who belongs to at least $n$ committees.Othershttp://gateoverflow.in/120576/isi-2016-pcb-c8Sun, 05 Mar 2017 09:12:44 +0000GATE2017-2-23
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 15:35:53 +0000How to Calculate No of Simple graph with labelled vertices?
http://gateoverflow.in/116256/how-to-calculate-no-of-simple-graph-with-labelled-vertices
<p>No of Simple Undirected Graph with unablled vertices - <strong>2<sup>nC2</sup></strong></p>
<p>No of Simple Undirected Graph with labelled vertices - ?</p>
<p>No of Simple Undirected Connected Graph with unablled vertices - ?</p>
<p>No of Simple Undirected Connected Graph with labelled vertices - ?</p>Programminghttp://gateoverflow.in/116256/how-to-calculate-no-of-simple-graph-with-labelled-verticesSun, 05 Feb 2017 18:24:08 +0000GRAPH TRAVERSALS
http://gateoverflow.in/115452/graph-traversals
WHY CROSS EDGES TURN TO BE BACK EDGES IN UNDIRECTED GRAPH IN DFS TRAVERSAL?? CAN ANYONE EXPLAIN THIS. WHY ARE THERE NO CROSS EDGES IN DFS OF UNDIRECTED GRAPH??Programminghttp://gateoverflow.in/115452/graph-traversalsFri, 03 Feb 2017 22:58:27 +0000graph theory , clique and isolated graph
http://gateoverflow.in/114715/graph-theory-clique-and-isolated-graph
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=3413708186731175028"></p>
<p>here in this question they have asked about the number of edges but i cant find a way to solve pls help here...</p>Othershttp://gateoverflow.in/114715/graph-theory-clique-and-isolated-graphThu, 02 Feb 2017 10:11:29 +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 22:46:17 +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-theoryTue, 31 Jan 2017 00:03:27 +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 22:01:57 +0000connected components madeeasy
http://gateoverflow.in/110510/connected-components-madeeasy
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13687870456048466528"></p>Algorithmshttp://gateoverflow.in/110510/connected-components-madeeasyTue, 24 Jan 2017 19:42:22 +0000Biconnected Components
http://gateoverflow.in/110412/biconnected-components
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=4209097371673567116"></p>
<p>Explain...?</p>Algorithmshttp://gateoverflow.in/110412/biconnected-componentsTue, 24 Jan 2017 16:28:43 +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 14:30:19 +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 20:29:48 +0000relation between vertex cover and independent set
http://gateoverflow.in/108220/relation-between-vertex-cover-and-independent-set
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14489833909619170802"></p>Algorithmshttp://gateoverflow.in/108220/relation-between-vertex-cover-and-independent-setFri, 20 Jan 2017 14:41:10 +0000Disconnected components
http://gateoverflow.in/107891/disconnected-components
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8859142765896571946"></p>Algorithmshttp://gateoverflow.in/107891/disconnected-componentsThu, 19 Jan 2017 15:41:36 +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 18:22:13 +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 18:15:46 +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-theoryWed, 18 Jan 2017 02:36:55 +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 19:24:25 +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 18:00:45 +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 11:50:45 +0000