GATE Overflow - Recent questions tagged graph-theory
https://gateoverflow.in/tag/graph-theory
Powered by Question2AnswerSelf Doubt ( Decrease key operation )
https://gateoverflow.in/160369/self-doubt-decrease-key-operation
While going through dijkstra's algorithm, there is a term "decrease key". I am not getting the meaning when it says "we do decrease key operation". What exactly we do and what is the meaning of decrease key ?Algorithmshttps://gateoverflow.in/160369/self-doubt-decrease-key-operationSun, 15 Oct 2017 16:49:25 +0000GATE2001-2.15 GATE1994-1.6
https://gateoverflow.in/159550/gate2001-2-15-gate1994-1-6
<p>How many undirected graphs are possible with n vertices</p>
<ol style="list-style-type: lower-alpha;">
<li>if graphs are not necessarily connected</li>
<li>if they are necessarily connected</li>
</ol>
<p> </p>Graph Theoryhttps://gateoverflow.in/159550/gate2001-2-15-gate1994-1-6Thu, 12 Oct 2017 17:38:24 +0000Preparation of Graph Theory
https://gateoverflow.in/154184/preparation-of-graph-theory
<p>Hello Sir, I have gone through the previous year questions and also gave some tests till now. From this experience I have realized that in <span class="marker"><strong>GRAPH THEORY - </strong></span><strong> almost 90% of the questions are theory based as a result I am not able to give the correct answer as I am not sure of the options in the given question. Hence whenever I see the question on Graphs Im simply skipping . Please provide some guidance and suggestions on how to get out of this situation and start understanding the subject answer the questions with confidence..</strong></p>
<p>Thank you</p>Study Resourceshttps://gateoverflow.in/154184/preparation-of-graph-theoryFri, 22 Sep 2017 08:21:37 +0000GATE 1987#Binary Tree
https://gateoverflow.in/154126/gate-1987%23binary-tree
<p><a rel="nofollow" href="http://gateoverflow.in/2604/gate1995_1-17">http://gateoverflow.in/2604/gate1995_1-17</a> .What is the degree of a node in a tree? Is it same as a graph OR the number of children of that node?</p>Programminghttps://gateoverflow.in/154126/gate-1987%23binary-treeFri, 22 Sep 2017 05:15:01 +0000graph theory
https://gateoverflow.in/153771/graph-theory
<p><strong>"A planar graph need not to be connected" </strong></p>
<p>Can someone plz explain with an example .</p>Set Theory & Algebrahttps://gateoverflow.in/153771/graph-theoryWed, 20 Sep 2017 18:33:56 +0000DYNAMIC PROGRAMMING
https://gateoverflow.in/153014/dynamic-programming
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=16999013844290231030"></p>Algorithmshttps://gateoverflow.in/153014/dynamic-programmingSun, 17 Sep 2017 19:34:26 +0000Graph Theory
https://gateoverflow.in/151990/graph-theory
Consider a 'reversed Kruskal' Algorithm for computing a MST. Initialize T to be the set of all edges in the graph. Now consider edges from largest to smallest cost. For each edge, delete it from T if that edge belongs to a cycle in T. Assuming all the edge costs are distinct, does this new algorithm correctly compute a MST?<br />
<br />
<br />
<br />
a) Yes<br />
<br />
b) no<br />
<br />
c) cant sayGraph Theoryhttps://gateoverflow.in/151990/graph-theoryThu, 14 Sep 2017 03:24:49 +0000Graph theory
https://gateoverflow.in/151874/graph-theory
The total number of non isomorphic graph which can be formed with 3 vertices________________________Graph Theoryhttps://gateoverflow.in/151874/graph-theoryWed, 13 Sep 2017 13:19:12 +0000How many simple path from u to v going through w?
https://gateoverflow.in/150924/how-many-simple-path-from-u-to-v-going-through-w
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?<br />
<br />
Please explain in detail. Thank you.Graph Theoryhttps://gateoverflow.in/150924/how-many-simple-path-from-u-to-v-going-through-wSat, 09 Sep 2017 10:25:01 +0000Graph theory-Relation.
https://gateoverflow.in/146142/graph-theory-relation
Can anyone explain "closure of relation" or share link for that.Mathematical Logichttps://gateoverflow.in/146142/graph-theory-relationMon, 21 Aug 2017 14:25:53 +0000Please solve this Q
https://gateoverflow.in/145638/please-solve-this-q
<p>Q. Consider the weighted undirected graph below</p>
<p> <img alt="" height="244" src="http://www.wooe.in/dashboard/img/Uploads/tumbnails/untitled%20folder/f-10-1.png" width="332"></p>
<p>Assume prim’s algorithm and kruskal’s algorithm are executed on the above graph to find the minimum spanning tree. For a particular edge (ei) which is included in minimum spanning tree and the position of an edge in minimum spanning tree is denoted by epi . Where 1?epi ? 8 (where position defines the order in which edges are included in the MST). Then what is the maximum value of <img alt="" height="50" src="http://www.wooe.in/dashboard/img/Uploads/tumbnails/untitled%20folder/f-10-2.png" width="241"></p>Algorithmshttps://gateoverflow.in/145638/please-solve-this-qSun, 20 Aug 2017 01:38:37 +0000Graph theory.
https://gateoverflow.in/145557/graph-theory
Matching and edge coloring are same ?Graph Theoryhttps://gateoverflow.in/145557/graph-theorySat, 19 Aug 2017 15:08:03 +0000Please solve this Q
https://gateoverflow.in/145105/please-solve-this-q
<p>Q. Consider the following adjacency matrix that represents undirected graph.</p>
<p> <img alt="" height="119" src="http://www.wooe.in/dashboard/img/Uploads/tumbnails/untitled%20folder%2010/016.png" width="122"></p>
<p>The minimum cost of the path whose destination is <em>D</em> where all vertices are covered exactly once in the path but it may start from any vertex other than <em>D</em> are </p>Algorithmshttps://gateoverflow.in/145105/please-solve-this-qFri, 18 Aug 2017 05:11:42 +0000Min Cut set
https://gateoverflow.in/145083/min-cut-set
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=731647461265627009"></p>Graph Theoryhttps://gateoverflow.in/145083/min-cut-setFri, 18 Aug 2017 03:45:25 +0000Please solve this Q
https://gateoverflow.in/144988/please-solve-this-q
<p>Q. Consider the weighted undirected graph with 4 vertices, where the weight of edge {i, j} g is given by the entry Wij in the matrix W<a rel="nofollow" href="http://www.geeksforgeeks.org/wp-content/uploads/gq/2016/02/gt164.png"><img alt="gt164" height="118" src="http://www.geeksforgeeks.org/wp-content/uploads/gq/2016/02/gt164.png" width="231"></a>The largest possible integer value of x, for which at least one shortest path between some pair of vertices will contain the edge with weight x is ________ Note : This question was asked as Numerical Answer Type.</p>
<p>A) 8</p>
<p>B) 12</p>
<p>C) 10</p>
<p>D) 11</p>Algorithmshttps://gateoverflow.in/144988/please-solve-this-qThu, 17 Aug 2017 15:45:00 +0000please solve this Q
https://gateoverflow.in/142533/please-solve-this-q
Q . The maximum number of edges in an undirected graph (simple) with 52 vertices and 3 components areGraph Theoryhttps://gateoverflow.in/142533/please-solve-this-qTue, 08 Aug 2017 18:20:38 +0000number of paths in a graph
https://gateoverflow.in/142407/number-of-paths-in-a-graph
Find the number of paths of length n between two different vertices in K4 if n is<br />
a) 2. b) 3. c) 4. d) 5.Mathematical Logichttps://gateoverflow.in/142407/number-of-paths-in-a-graphTue, 08 Aug 2017 05:38:07 +0000Number of Hamiltonian cycles in a complete graph
https://gateoverflow.in/140260/number-of-hamiltonian-cycles-in-a-complete-graph
Number of Hamilton cycles in a complete labelled graph?Graph Theoryhttps://gateoverflow.in/140260/number-of-hamiltonian-cycles-in-a-complete-graphThu, 27 Jul 2017 22:11:35 +0000maximum value of n to be deadlock
https://gateoverflow.in/137867/maximum-value-of-n-to-be-deadlock
A computer system has 6 tape drives, with n processes competing for them. Each process may need 3 tape drives. What is the maximum value of n for which the system is guaranteed to be deadlock? Justify your answer.Operating Systemhttps://gateoverflow.in/137867/maximum-value-of-n-to-be-deadlockFri, 14 Jul 2017 17:29:19 +0000graph theory
https://gateoverflow.in/136745/graph-theory
can we say a null graph is eulerian circuit and hamiltonian circuit?Mathematical Logichttps://gateoverflow.in/136745/graph-theorySat, 08 Jul 2017 14:02:39 +0000Rosen
https://gateoverflow.in/136736/rosen
Find the edge chromatic numbers of<br />
a) Cn, where n ≥ 3. (Cycle with n vertices)<br />
<br />
b) Wn, where n ≥ 3 (Wheel with n vertices)<br />
<br />
c)Complete graph with n vertices.Engineering Mathematicshttps://gateoverflow.in/136736/rosenSat, 08 Jul 2017 13:26:57 +0000graph
https://gateoverflow.in/136184/graph
a tree with n vertices can have at most 1 perfect matching how?<br />
<br />
<br />
<br />
<br />
<br />
perfect matching means no vertices will be left with 0 dergree right so how a tree can have a perfect matching <br />
<br />
explain with the help of trees plzMathematical Logichttps://gateoverflow.in/136184/graphWed, 05 Jul 2017 14:21:29 +0000Graph Degree sequence : Bondy and Murty : $1.1.16$
https://gateoverflow.in/136078/graph-degree-sequence-bondy-and-murty-%241-1-16%24
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:<br />
<br />
there is a loopless graph with degree sequence d if and only if $\sum_{i=1}^{n}d_i$ is even and $d_1 \leq \sum_{i=2}^{n}d_i$Graph Theoryhttps://gateoverflow.in/136078/graph-degree-sequence-bondy-and-murty-%241-1-16%24Wed, 05 Jul 2017 01:06:47 +0000Graph Theory : Bondy-Murty $1.1.20$
https://gateoverflow.in/136075/graph-theory-bondy-murty-%241-1-20%24
<p>Let $S$ be a set of $n$ points in the plane, the distance between any two of which is at least one. Show that there are at most $3n$ pairs of points of S at distance exactly one.</p>
<p> </p>
<p>Can this be done with a <strong>unit circle</strong> and we can place at max. $6$ points on the perimeter and doing the same for other points as well ? i.e. we can get $6n/2 = 3n$ pairs at max. ?
<br>
</p>Graph Theoryhttps://gateoverflow.in/136075/graph-theory-bondy-murty-%241-1-20%24Wed, 05 Jul 2017 00:55:34 +0000Graphic Sequence condition
https://gateoverflow.in/136045/graphic-sequence-condition
<p>A sequence $d = (d_1,d_2,\dots , d_n)$ is <strong><em>graphic</em></strong> if there is a simple graph with degree sequence $d$</p>
<p>If $d = (d_1,d_2,d_3, \dots d_n)$ is graphic and $d_1 \geq d_2 \geq d_3 \geq \dots \geq d_n$ , then show that $\sum_{i=1}^{n}d_i$ is even and $$\sum_{i=1}^{k}d_i \leq \left [ k(k-1) + \sum_{i=k+1}^{n} \min\{k,d_i\} \right ] \quad ,1 \leq k \leq n$$.</p>
<p> </p>Graph Theoryhttps://gateoverflow.in/136045/graphic-sequence-conditionTue, 04 Jul 2017 14:13:13 +0000Minimum No. of vertices required
https://gateoverflow.in/135641/minimum-no-of-vertices-required
<p>Prove the following for graph $G$.</p>
<ol>
<li>When length of the <strong><em>shortest cycle</em></strong> in a graph is $k \geq 3$ and the minimum degree of the graph is $d$, then $G$ has minimum $\begin{align*} \\ 1+ \sum_{0 \leq p < \left \lfloor k/2 \right \rfloor} d\cdot (d-1)^p \end{align*}$ vertices for <strong>odd</strong> $k$.</li>
<li>When the length of the <strong><em>shortest cycle</em></strong> in a graph is $k \geq 4$ and the minimum degree of the graph is $d$, then $G$ has minimum $\begin{align*} \\1+ (d-1)^{\left \lfloor k/2 \right \rfloor -1} + \sum_{0 \leq p < \left \lfloor k/2 \right \rfloor-1} d\cdot (d-1)^p \end{align*}$ vertices for <strong>even </strong>$k$. </li>
</ol>Graph Theoryhttps://gateoverflow.in/135641/minimum-no-of-vertices-requiredSat, 01 Jul 2017 19:27:17 +0000Diameter of a graph and tree
https://gateoverflow.in/133949/diameter-of-a-graph-and-tree
Why there is a difference between diameter of a graph and tree?<br />
<br />
Diameter of a tree as i have read is the maximum path between two vertices(number of edges between two vertices)<br />
<br />
But for tree it says number of nodes on the longest path.<br />
<br />
But tree is a graph so why cant i find the diameter of tree in similar way?Mathematical Logichttps://gateoverflow.in/133949/diameter-of-a-graph-and-treeTue, 20 Jun 2017 01:43:39 +0000Self - Doubt
https://gateoverflow.in/133883/self-doubt
What is clique?Graph Theoryhttps://gateoverflow.in/133883/self-doubtMon, 19 Jun 2017 13:44:27 +0000[Discrete Maths] Graph Theory Rosen,Chromatic number
https://gateoverflow.in/132851/discrete-maths-graph-theory-rosen-chromatic-number
<p>What are the chromatic number of following graphs?</p>
<p> </p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2427432278983743495"></p>
<p>Answer is 6 and 4 respectively.But i am getting 3 for both.</p>
<p>Please someone confirm this?</p>Mathematical Logichttps://gateoverflow.in/132851/discrete-maths-graph-theory-rosen-chromatic-numberTue, 13 Jun 2017 03:38:59 +0000Discrete Maths Graph theory
https://gateoverflow.in/132838/discrete-maths-graph-theory
What are the necessary and sufficient conditions for Euler path and Circuit in directed graph?Mathematical Logichttps://gateoverflow.in/132838/discrete-maths-graph-theoryTue, 13 Jun 2017 01:37:24 +0000[Discrete maths] graph theory Perfect matching
https://gateoverflow.in/132353/discrete-maths-graph-theory-perfect-matching
When matching number and covering number are same then can we say that it is a perfect matching case?Do i need to check the elements of the set( edges in both matching and covering) also if their cardinality is same?If yes,then can someone give me an example where matching number and covering number same but still it is not a perfect match?I am not able to find such a case and i think it will not exist.Mathematical Logichttps://gateoverflow.in/132353/discrete-maths-graph-theory-perfect-matchingThu, 08 Jun 2017 20:41:26 +0000[Discrete Maths] Graph theory
https://gateoverflow.in/132276/discrete-maths-graph-theory
What is the vertex connectivity and edge connectivity of complete graph?<br />
<br />
Is it n or n-1?Graph Theoryhttps://gateoverflow.in/132276/discrete-maths-graph-theoryWed, 07 Jun 2017 22:18:24 +0000Graphs
https://gateoverflow.in/130806/graphs
Maximum degree of any vertex in a single graph of vertices n is?<br />
<br />
a. none of the above<br />
<br />
b. n<br />
<br />
c. n-1<br />
<br />
d. n+1<br />
<br />
e. 2n-1Programminghttps://gateoverflow.in/130806/graphsThu, 25 May 2017 23:53:30 +0000graphtheory,Narsingh Deo,4.26
https://gateoverflow.in/130286/graphtheory-narsingh-deo-4-26
Suppose a single tennis tournament is arranged among n players and the number of matches planned is a fixed number e (where n-1 < e < n(n-1)/2 ).For sake of fairness,how will you make sure that some players do not group together and isolate an individual (or a group of players).Graph Theoryhttps://gateoverflow.in/130286/graphtheory-narsingh-deo-4-26Sun, 21 May 2017 03:34:20 +0000#Graphtheory
https://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 Theoryhttps://gateoverflow.in/130285/%23graphtheorySun, 21 May 2017 02:56:10 +00002 - connected graph
https://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 Theoryhttps://gateoverflow.in/130141/2-connected-graphFri, 19 May 2017 07:12:05 +0000Isomorphism and subgraph
https://gateoverflow.in/130078/isomorphism-and-subgraph
If there are two graphs G1 and G2 and both are Isomorphic to each other...Is G1 subset of G2?Graph Theoryhttps://gateoverflow.in/130078/isomorphism-and-subgraphThu, 18 May 2017 15:21:51 +0000GATE Graph Theory
https://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 Theoryhttps://gateoverflow.in/129447/gate-graph-theoryFri, 12 May 2017 19:24:26 +0000Graph Theory
https://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 Theoryhttps://gateoverflow.in/129355/graph-theoryFri, 12 May 2017 08:04:59 +0000Graph theory and Applications Bondy and Murty Exercise Qn 1.9
https://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 Theoryhttps://gateoverflow.in/129036/graph-theory-and-applications-bondy-and-murty-exercise-qn-1Tue, 09 May 2017 16:09:49 +0000keneth r rosen
https://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 Theoryhttps://gateoverflow.in/128471/keneth-r-rosenSun, 07 May 2017 13:28:40 +0000Relation between k and k-1 edge connected graph
https://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.Algorithmshttps://gateoverflow.in/128029/relation-between-k-and-k-1-edge-connected-graphWed, 03 May 2017 23:36:19 +0000PGEE 2017
https://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 Theoryhttps://gateoverflow.in/127521/pgee-2017Sun, 30 Apr 2017 18:04:30 +0000PGEE 2017
https://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 y<br />
<br />
Which vertex will have highest in degree ?Graph Theoryhttps://gateoverflow.in/127520/pgee-2017Sun, 30 Apr 2017 18:00:23 +0000PGEE 2017
https://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 Theoryhttps://gateoverflow.in/127519/pgee-2017Sun, 30 Apr 2017 17:58:18 +0000Self-Doubt
https://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 Theoryhttps://gateoverflow.in/126868/self-doubtTue, 25 Apr 2017 06:41:09 +0000graph theory
https://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 Theoryhttps://gateoverflow.in/124669/graph-theoryFri, 07 Apr 2017 17:38:26 +0000ISI Entrance Exam MTech (CS)
https://gateoverflow.in/124367/isi-entrance-exam-mtech-cs
Consider all possible trees with $n$ nodes. Let $k$ be the number of nodes with degree greater than $1$ in a given tree. What is the maximum possible value of $k$?Graph Theoryhttps://gateoverflow.in/124367/isi-entrance-exam-mtech-csThu, 06 Apr 2017 00:52:41 +0000Graph Theory
https://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 proofAlgorithmshttps://gateoverflow.in/123618/graph-theorySun, 02 Apr 2017 22:12:23 +0000