GATE Overflow - Recent questions in Graph Theory
http://gateoverflow.in/questions/mathematics/discrete-mathematics/graph-theory
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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 12:08:26 +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-csWed, 05 Apr 2017 19:22:41 +0000JNUEE-2016
http://gateoverflow.in/123807/jnuee-2016
Consider an undirected graph G with 100 nodes. What is the maximum number of edges to be included in G so that graph is connected?<br />
<br />
(a) 2451<br />
<br />
(b) 4851<br />
<br />
(c) 4950<br />
<br />
(d) 9990Graph Theoryhttp://gateoverflow.in/123807/jnuee-2016Mon, 03 Apr 2017 15:39:51 +0000cil 2017
http://gateoverflow.in/123566/cil-2017
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12137641003618320025"></p>
<p>a. 2</p>
<p>b. 4</p>
<p>c. 1</p>
<p>d. 3</p>Graph Theoryhttp://gateoverflow.in/123566/cil-2017Sun, 02 Apr 2017 11:58:21 +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-pathSat, 01 Apr 2017 20:50:33 +0000Consider a graph of only 1 vertex and no edges. Is it connected or disconnected?
http://gateoverflow.in/122976/consider-graph-only-vertex-and-edges-connected-disconnected
Graph Theoryhttp://gateoverflow.in/122976/consider-graph-only-vertex-and-edges-connected-disconnectedThu, 30 Mar 2017 07:53:42 +0000Suppose a graph G with n vertices is isomorphic to its complement.How many edges does G have?
http://gateoverflow.in/122925/suppose-graph-vertices-isomorphic-complement-many-edges-does
Graph Theoryhttp://gateoverflow.in/122925/suppose-graph-vertices-isomorphic-complement-many-edges-doesWed, 29 Mar 2017 17:31:21 +0000Graph_Theory
http://gateoverflow.in/122276/graph_theory
Determine all non- isomorphic graphs with the number of vertices 20 and edges 188.Graph Theoryhttp://gateoverflow.in/122276/graph_theoryTue, 21 Mar 2017 09:45:08 +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 07:40:09 +0000radius ,diameter of graph
http://gateoverflow.in/121818/radius-diameter-of-graph
The distance between two distinct vertices v1 and v2 of a<br />
connected simple graph is the length (number of edges) of<br />
the shortest path between v1 and v2. The radius of a graph<br />
is the minimum over all vertices v of the maximum distance<br />
from v to another vertex. The diameter of a graph<br />
is the maximum distance between two distinct vertices.<br />
Find the radius and diameter of<br />
a) K6. b) K4,5. c) Q3. d) C6.Graph Theoryhttp://gateoverflow.in/121818/radius-diameter-of-graphThu, 16 Mar 2017 11:23:23 +0000Rosen ex.55 chp 8
http://gateoverflow.in/121595/rosen-ex-55-chp-8
If the simple graph G has v vertices and e edges, how many edges does G complement have?Graph Theoryhttp://gateoverflow.in/121595/rosen-ex-55-chp-8Tue, 14 Mar 2017 16:11:53 +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 12:22:08 +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 11:23:30 +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 11:20:02 +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 05:27:10 +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 04:46:37 +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 13:36:22 +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 04:33:49 +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 15:55:28 +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 04:55:56 +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 04:40:12 +0000Walk in Graph Theory
http://gateoverflow.in/121022/walk-in-graph-theory
<p>In Narsingh Deo, Walk is defined as "no edge appears (is covered or traversed) in more than 1 walk" but I studied that walk can have repeated edges. Is there a mistake in Narsingh Deo or I am missing some point?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12352650482047581356"></p>Graph Theoryhttp://gateoverflow.in/121022/walk-in-graph-theoryWed, 08 Mar 2017 20:01:59 +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 15:05:19 +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 15:01:38 +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 14:52:47 +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 01:52:42 +0000narsingh deo
http://gateoverflow.in/119875/narsingh-deo
In a village there are equal no of boys and girls of marriageable age.Each boy dates a certain no. of girls and each girl dates a certain number of boys,under what condition is it possible that every girl and boy gets married to one of their dates?Graph Theoryhttp://gateoverflow.in/119875/narsingh-deoMon, 27 Feb 2017 03:49:57 +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 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 +0000