GATE Overflow - Recent questions tagged graph-theory
http://gateoverflow.in/tag/graph-theory
Powered by Question2AnswerDiameter 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<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 +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 +0000