GATE Overflow - Recent questions tagged graph-theory
http://gateoverflow.in/tag/graph-theory
Powered by Question2AnswerGraph theory-Relation.
http://gateoverflow.in/146142/graph-theory-relation
Can anyone explain "closure of relation" or share link for that.Mathematical Logichttp://gateoverflow.in/146142/graph-theory-relationMon, 21 Aug 2017 14:25:53 +0000Please solve this Q
http://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>Algorithmshttp://gateoverflow.in/145638/please-solve-this-qSun, 20 Aug 2017 01:38:37 +0000Graph theory.
http://gateoverflow.in/145557/graph-theory
Matching and edge coloring are same ?Graph Theoryhttp://gateoverflow.in/145557/graph-theorySat, 19 Aug 2017 15:08:03 +0000Please solve this Q
http://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>Algorithmshttp://gateoverflow.in/145105/please-solve-this-qFri, 18 Aug 2017 05:11:42 +0000Min Cut set
http://gateoverflow.in/145083/min-cut-set
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=731647461265627009"></p>Graph Theoryhttp://gateoverflow.in/145083/min-cut-setFri, 18 Aug 2017 03:45:25 +0000Please solve this Q
http://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>Algorithmshttp://gateoverflow.in/144988/please-solve-this-qThu, 17 Aug 2017 15:45:00 +0000please solve this Q
http://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 Theoryhttp://gateoverflow.in/142533/please-solve-this-qTue, 08 Aug 2017 18:20:38 +0000number of paths in a graph
http://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 Logichttp://gateoverflow.in/142407/number-of-paths-in-a-graphTue, 08 Aug 2017 05:38:07 +0000Number of Hamiltonian cycles in a complete graph
http://gateoverflow.in/140260/number-of-hamiltonian-cycles-in-a-complete-graph
Number of Hamilton cycles in a complete labelled graph?Graph Theoryhttp://gateoverflow.in/140260/number-of-hamiltonian-cycles-in-a-complete-graphThu, 27 Jul 2017 22:11:35 +0000maximum value of n to be deadlock
http://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 Systemhttp://gateoverflow.in/137867/maximum-value-of-n-to-be-deadlockFri, 14 Jul 2017 17:29:19 +0000graph theory
http://gateoverflow.in/136745/graph-theory
can we say a null graph is eulerian circuit and hamiltonian circuit?Mathematical Logichttp://gateoverflow.in/136745/graph-theorySat, 08 Jul 2017 14:02:39 +0000Rosen
http://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 Mathematicshttp://gateoverflow.in/136736/rosenSat, 08 Jul 2017 13:26:57 +0000graph
http://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 Logichttp://gateoverflow.in/136184/graphWed, 05 Jul 2017 14:21:29 +0000Graph Degree sequence : Bondy and Murty : $1.1.16$
http://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 Theoryhttp://gateoverflow.in/136078/graph-degree-sequence-bondy-and-murty-%241-1-16%24Wed, 05 Jul 2017 01:06:47 +0000Graph Theory : Bondy-Murty $1.1.20$
http://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 Theoryhttp://gateoverflow.in/136075/graph-theory-bondy-murty-%241-1-20%24Wed, 05 Jul 2017 00:55:34 +0000Graphic Sequence condition
http://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 Theoryhttp://gateoverflow.in/136045/graphic-sequence-conditionTue, 04 Jul 2017 14:13:13 +0000Minimum No. of vertices required
http://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 Theoryhttp://gateoverflow.in/135641/minimum-no-of-vertices-requiredSat, 01 Jul 2017 19:27:17 +0000Diameter of a graph and tree
http://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 Logichttp://gateoverflow.in/133949/diameter-of-a-graph-and-treeTue, 20 Jun 2017 01:43:39 +0000Self - Doubt
http://gateoverflow.in/133883/self-doubt
What is clique?Graph Theoryhttp://gateoverflow.in/133883/self-doubtMon, 19 Jun 2017 13:44:27 +0000[Discrete Maths] Graph Theory Rosen,Chromatic number
http://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 Logichttp://gateoverflow.in/132851/discrete-maths-graph-theory-rosen-chromatic-numberTue, 13 Jun 2017 03:38:59 +0000Discrete Maths Graph theory
http://gateoverflow.in/132838/discrete-maths-graph-theory
What are the necessary and sufficient conditions for Euler path and Circuit in directed graph?Mathematical Logichttp://gateoverflow.in/132838/discrete-maths-graph-theoryTue, 13 Jun 2017 01:37:24 +0000[Discrete maths] graph theory Perfect matching
http://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 Logichttp://gateoverflow.in/132353/discrete-maths-graph-theory-perfect-matchingThu, 08 Jun 2017 20:41:26 +0000[Discrete Maths] Graph theory
http://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 Theoryhttp://gateoverflow.in/132276/discrete-maths-graph-theoryWed, 07 Jun 2017 22:18:24 +0000Graphs
http://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-1Programminghttp://gateoverflow.in/130806/graphsThu, 25 May 2017 23:53:30 +0000graphtheory,Narsingh Deo,4.26
http://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 Theoryhttp://gateoverflow.in/130286/graphtheory-narsingh-deo-4-26Sun, 21 May 2017 03:34:20 +0000#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 +0000Isomorphism and subgraph
http://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 Theoryhttp://gateoverflow.in/130078/isomorphism-and-subgraphThu, 18 May 2017 15:21:51 +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 y<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 of nodes with degree greater than $1$ in a given tree. What is 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 +0000