GATE Overflow - Recent questions tagged graph-connectivity
http://gateoverflow.in/tag/graph-connectivity
Powered by Question2Answer[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
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 +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
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 +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 +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 +0000Graph Theory Me workbook
http://gateoverflow.in/115573/graph-theory-me-workbook
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=223024569878688878"></p>
<p>How S2 is correct ,I can have more than n-k edges like if n=7 and k=3 ,then K1(a-b-c-d-e) k2(f() k2(g).K1,k2,k3 are different compoinents i assumes,Now in K1 i can add one more edge between a to c or a to d and still it will be simple graph and it will have 3 components?Please help</p>Set Theory & Algebrahttp://gateoverflow.in/115573/graph-theory-me-workbookSat, 04 Feb 2017 10:58:17 +0000graph theory
http://gateoverflow.in/100206/graph-theory
Assumed undirected graph G is connected. G has 6vertices and 10 edges. Find<br />
the minimum number of edges whose deletion from graph G is always guarantee<br />
that it will become disconnected.Graph Theoryhttp://gateoverflow.in/100206/graph-theoryWed, 04 Jan 2017 02:27:09 +0000graph theory
http://gateoverflow.in/97768/graph-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11696266218365235197"></p>Graph Theoryhttp://gateoverflow.in/97768/graph-theoryWed, 28 Dec 2016 19:18:36 +0000graph
http://gateoverflow.in/92032/graph
Which of the following statements is/are TRUE?<br />
[P] Every disconnected graph has an isolated vertex<br />
[Q] A graph is connected if and only if some vertex is connected to all other vertices<br />
[R] The edge set of every closed trail can be partitioned into edge sets of cycles<br />
[S] If a maximal trail in a graph is not closed, then its endpoints have odd degreeGraph Theoryhttp://gateoverflow.in/92032/graphMon, 12 Dec 2016 16:20:24 +0000Graph theory
http://gateoverflow.in/92030/graph-theory
proof :- A connected graph any two paths of maximum length share at least one vertexGraph Theoryhttp://gateoverflow.in/92030/graph-theoryMon, 12 Dec 2016 16:09:47 +0000graph theory
http://gateoverflow.in/84795/graph-theory
Which of the following statements is/are TRUE?<br />
[P] Every disconnected graph has an isolated vertex<br />
[Q] A graph is connected if and only if some vertex is connected to all other vertices<br />
[R] The edge set of every closed trail can be partitioned into edge sets of cycles<br />
[S] If a maximal trail in a graph is not closed, then its endpoints have odd degreeGraph Theoryhttp://gateoverflow.in/84795/graph-theoryTue, 22 Nov 2016 12:55:21 +0000GATE1990-1-viii
http://gateoverflow.in/83854/gate1990-1-viii
Fill in the blanks:<br />
<br />
A graph which has the same number of edges as its complement must have number of vertices congruent to ________ or ________ modulo 4.Graph Theoryhttp://gateoverflow.in/83854/gate1990-1-viiiSat, 19 Nov 2016 00:36:49 +0000Doubt: Graph Theory
http://gateoverflow.in/80069/doubt-graph-theory
When say that with n vertices there are total 2^(n(n-1)/2) connected/disconnected graph possible, in this case we are assuming that vertices are labelled, right??<br />
<br />
<br />
<br />
Is there any formula to count number of connected/disconnected graphs possible with n unlabeled vertices?Graph Theoryhttp://gateoverflow.in/80069/doubt-graph-theoryTue, 08 Nov 2016 08:41:14 +0000Kerala PSC AP Exam
http://gateoverflow.in/77267/kerala-psc-ap-exam
The maximum number of edges in an acyclic undirected graph with n vertices<br />
<br />
A) n - 1<br />
<br />
B) n<br />
<br />
C) n +1<br />
<br />
D) 2n -1DShttp://gateoverflow.in/77267/kerala-psc-ap-examThu, 27 Oct 2016 22:23:07 +0000Graph theory
http://gateoverflow.in/76955/graph-theory
Decomposition of complete graph into cycles through all vertices.<br />
Continuing explanation [here][1],<br />
Next explanation is given as<br />
<br />
for $n=5$ , $n=7$, it suffices to use cycles formed by traversing the<br />
vertices with constant difference:$\left(0,1,2,3,4\right)$,$\left(0,2,4,1,3\right)$ for $n=5 $<br />
<br />
and<br />
<br />
$\left(0,1,2,3,4,5,6\right)$,$\left(0,3,6,2,5,1,4\right)$ for $n=7 $<br />
<br />
Not getting how <br />
$\left(0,1,2,3,4\right)$,$\left(0,2,4,1,3\right)$ and $\left(0,1,2,3,4,5,6\right)$,$\left(0,3,6,2,5,1,4\right)$ is coming from !!!!!<br />
<br />
Please help me out!!<br />
<br />
[1]: <a href="http://math.stackexchange.com/questions/1985647/decomposition-of-complete-graph-into-cycles-through-all-vertices/1985652#1985652" rel="nofollow" target="_blank">http://math.stackexchange.com/questions/1985647/decomposition-of-complete-graph-into-cycles-through-all-vertices/1985652#1985652</a>Graph Theoryhttp://gateoverflow.in/76955/graph-theoryWed, 26 Oct 2016 17:59:26 +0000Graph connectivity
http://gateoverflow.in/73128/graph-connectivity
<p><img alt="Loading Question" src="https://d2190hpfa85jkd.cloudfront.net/q/aa27563a2b91fc7079e234e2873059f7.jpg"></p>Graph Theoryhttp://gateoverflow.in/73128/graph-connectivityMon, 10 Oct 2016 18:23:34 +0000Gatebook
http://gateoverflow.in/63846/gatebook
<h2>Let A has n vertices. If Ā is connected graph then the maximum number of edges that A can have is</h2>
<h3>a) (n-1)(n-2)/2
<br>
b) n(n-1)/2
<br>
c) n-1
<br>
d) n</h3>Mathematical Logichttp://gateoverflow.in/63846/gatebookFri, 19 Aug 2016 17:03:49 +0000Graph Theory
http://gateoverflow.in/62888/graph-theory
consider the following statement-:<br />
<br />
1.If a graph has Euler circuit then it is Strongly Connected graph.<br />
<br />
2.If a graph has Euler path(but not Euler circuit) then it is Strongly Connected graph.<br />
<br />
3.If a graph has Euler circuit then it is Weakly Connected graph.<br />
<br />
4.If a graph has Euler path(but not euler circuit) then it is Weakly Connected graph.<br />
<br />
Which statement is true with proper explanation.Graph Theoryhttp://gateoverflow.in/62888/graph-theoryFri, 12 Aug 2016 10:09:13 +0000Graph theory
http://gateoverflow.in/62654/graph-theory
complement of a complete bipartite graph Km,n .please provide a figure for explanation.Graph Theoryhttp://gateoverflow.in/62654/graph-theoryWed, 10 Aug 2016 17:36:35 +0000UGCNET-Sep2013-II-20
http://gateoverflow.in/49362/ugcnet-sep2013-ii-20
<p>Consider the following statements:</p>
<ol style="list-style-type: upper-roman;">
<li>A graph in which there is a unique path between every pair of vertices is a tree.</li>
<li>A connected graph with e=v-1 is a tree</li>
<li>A connected graph with e=v-1 that has no circuit is a tree</li>
</ol>
<p>Which one of the above statements is/are true?</p>
<ol style="list-style-type: upper-alpha;">
<li>I and III</li>
<li>II and III</li>
<li>I and II</li>
<li>All of the above</li>
</ol>
DShttp://gateoverflow.in/49362/ugcnet-sep2013-ii-20Thu, 09 Jun 2016 13:14:47 +0000CMI2011-B-01b
http://gateoverflow.in/47092/cmi2011-b-01b
A multinational company is developing an industrial area with many buildings. They want to connect the buildings with a set of roads so that:<br />
<br />
Each road connects exactly two buildings.<br />
<br />
Any two buildings are connected via a sequence of roads.<br />
<br />
Omitting any road leads to at least two buildings not being connected by any sequence of roads.<br />
<br />
Two roads are said to be $adjacent$ to each other if they serve a common building. A set of roads is said to be $preferred$ if:<br />
<br />
No two roads in the set are adjacent, and,<br />
<br />
Each building is served by at least one road in the set.<br />
<br />
(ii) Is it always possible to find a preferred set of roads?<br />
<br />
(iii) Is it ever possible to find two sets of preferred roads differing in at least one road?<br />
<br />
Substantiate your answers by either proving the assertion or providing a counterexample.Graph Theoryhttp://gateoverflow.in/47092/cmi2011-b-01bFri, 27 May 2016 13:51:42 +0000CMI2011-B-02c
http://gateoverflow.in/47082/cmi2011-b-02c
<p>Let $G$ be a connected graph. For a vertex $x$ of $G$ we denote by $G−x$ the graph formed by removing $x$ and all edges incident on $x$ from $G$. $G$ is said to be good if there are at least two distinct vertices $x, y$ in $G$ such that both $G − x$ and $G − y$ are connected.</p>
<ol style="list-style-type:lower-roman">
<li>Show that there exists a graph $H$ such that we cannot find three distinct vertices $u_1, u_2, u_3$ such that each of $G − u_1,\: G − u_2,\: \text{ and } \: G − u_3$ is connected.</li>
</ol>
<p> </p>Graph Theoryhttp://gateoverflow.in/47082/cmi2011-b-02cFri, 27 May 2016 13:37:24 +0000CMI2011-B-02b
http://gateoverflow.in/47081/cmi2011-b-02b
<p style="line-height: 20.8px;">Let $G$ be a connected graph. For a vertex $x$ of $G$ we denote by $G−x$ the graph formed by removing $x$ and all edges incident on $x$ from $G$. $G$ is said to be good if there are at least two distinct vertices $x, y$ in $G$ such that both $G − x$ and $G − y$ are connected.</p>
<ol style="line-height: 20.8px; list-style-type: lower-roman;">
<li>Given a good graph, devise a linear time algorithm to find two such vertices.</li>
</ol>
<p style="line-height: 20.8px;"> </p>
Graph Theoryhttp://gateoverflow.in/47081/cmi2011-b-02bFri, 27 May 2016 13:37:07 +0000CMI2013-B-03
http://gateoverflow.in/46613/cmi2013-b-03
A simple graph is one in which there are no self loops and each pair of distinct vertices is connected by at most one edge. Show that any finite simple graph has at least two vertices with the same degree.Graph Theoryhttp://gateoverflow.in/46613/cmi2013-b-03Mon, 23 May 2016 14:36:19 +0000CMI2012-B-01
http://gateoverflow.in/46545/cmi2012-b-01
Let $G=(V, E)$ be a graph where $|V| =n$ and the degree of each vertex is strictly greater than $\frac{n}{2}$. Prove that $G$ has a Hamiltonian path. (Hint: Consider a path of maximum length in $G$.)Graph Theoryhttp://gateoverflow.in/46545/cmi2012-b-01Mon, 23 May 2016 05:32:16 +0000CMI2011-B-02a
http://gateoverflow.in/46203/cmi2011-b-02a
<p>Let $G$ be a connected graph. For a vertex $x$ of $G$ we denote by $G−x$ the graph formed by removing $x$ and all edges incident on $x$ from $G$. $G$ is said to be good if there are at least two distinct vertices $x, y$ in $G$ such that both $G − x$ and $G − y$ are connected.</p>
<ol style="list-style-type: lower-roman;">
<li>Show that for any subgraph $H$ of $G$, $H$ is good if and only if $G$ is good.</li>
</ol>
Set Theory & Algebrahttp://gateoverflow.in/46203/cmi2011-b-02aThu, 19 May 2016 11:59:10 +0000CMI2011-A-07
http://gateoverflow.in/46194/cmi2011-a-07
<p>Let $G=(V, E)$ be a graph. Define $\bar{G}$ to be $(V, \bar{E})$, where for all $u, \: v \: \in V \: , (u, v) \in \bar{E}$ if and only if $(u, v) \notin E$. Then which of the following is true?</p>
<ol style="list-style-type: upper-alpha;">
<li>$\bar{G}$ is always connected.</li>
<li>$\bar{G}$ is connected if $G$ is not connected.</li>
<li>At least one of $G$ and $\bar{G}$ connected.</li>
<li>$G$ is not connected or $\bar{G}$ is not connected</li>
</ol>
Graph Theoryhttp://gateoverflow.in/46194/cmi2011-a-07Thu, 19 May 2016 11:40:12 +0000CMI2010-B-02
http://gateoverflow.in/46129/cmi2010-b-02
<p><span style="line-height: 20.8px;">Let $G$ be a graph in which each vertex has degree at least $k$. Show that there is a path of length $k$ in $G$—that is, a sequence of $k+1$ distinct vertices $v_0, v_1, \dots v_k$ such that for $0 \leq i < k,$ $v_i$ is connected to $v_{i+1}$ in $G$.</span></p>
Graph Theoryhttp://gateoverflow.in/46129/cmi2010-b-02Thu, 19 May 2016 06:18:54 +0000Connectivity Graph Theory
http://gateoverflow.in/45037/connectivity-graph-theory
Which of the following statements are true . Please explain why each statement is true/false..<br />
<br />
S1 : If a simple graph G is not connected then it's complement G is not connected<br />
<br />
S2 : If a simple graph G is connected them it's complement G is not connected<br />
<br />
S3 : A simple graph with n vertices is necessarily connected if min degree of a vertex = (n-1)/2<br />
<br />
S4 : If a simple graph has exactly two vertices of odd degree then there exists a path between two vertices of odd degreeGraph Theoryhttp://gateoverflow.in/45037/connectivity-graph-theoryFri, 06 May 2016 18:07:19 +0000GATE2006-73
http://gateoverflow.in/43567/gate2006-73
The $2^n$ vertices of a graph G corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements.<br />
<br />
The number of connected components in G is:<br />
<br />
$n$<br />
<br />
$n + 2$<br />
<br />
$2^{n/2}$<br />
<br />
$\frac{2^{n}}{n}$Graph Theoryhttp://gateoverflow.in/43567/gate2006-73Sun, 24 Apr 2016 08:01:17 +0000TIFR2015-B-5
http://gateoverflow.in/29858/tifr2015-b-5
<p>Suppose
<br>
<br>
$\begin{pmatrix}
<br>
0&1 &0&0&0&1 \\
<br>
1&0&1&0&0&0 \\
<br>
0&1&0&1&0&1 \\
<br>
0&0&1&0&1&0 \\
<br>
0&0&0&1&0&1 \\
<br>
1&0&1&0&1&0
<br>
\end{pmatrix}$
<br>
<br>
is the adjacency matrix of an undirected graph with six vertices: that is, the rows and columns are indexed by vertices of the graph, and an entry is $1$ if the corresponding vertices are connected by an edge and is $0$ otherwise; the same order of vertices is used for the rows and columns. Which of the graphs below has the above adjacency matrix?</p>
<ol style="list-style-type:upper-alpha">
<li>Only $(i)$</li>
<li>Only $(ii)$</li>
<li>Only $(iii)$</li>
<li>Only $(iv)$</li>
<li>$(i)$ and $(ii)$</li>
</ol>Graph Theoryhttp://gateoverflow.in/29858/tifr2015-b-5Mon, 07 Dec 2015 18:15:45 +0000GATE2015-1_54
http://gateoverflow.in/8364/gate2015-1_54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.Graph Theoryhttp://gateoverflow.in/8364/gate2015-1_54Sat, 14 Feb 2015 04:55:13 +0000GATE2015-2_50
http://gateoverflow.in/8252/gate2015-2_50
<p>In a connected graph, a bridge is an edge whose removal disconnects the graph. Which one of the following statements is true?</p>
<p> </p>
<ol style="list-style-type:upper-alpha">
<li>A tree has no bridges</li>
<li>A bridge cannot be part of a simple cycle</li>
<li>Every edge of a clique with size ≥ 3 is a bridge (A clique is any complete subgraph of a graph)</li>
<li>A graph with bridges cannot have cycle</li>
</ol>
Graph Theoryhttp://gateoverflow.in/8252/gate2015-2_50Fri, 13 Feb 2015 09:42:54 +0000GATE2005-IT-56
http://gateoverflow.in/3817/gate2005-it-56
<p>Let G be a directed graph whose vertex set is the set of numbers from 1 to 100. There is an edge from a vertex i to a vertex j iff either j = i + 1 or j = 3i. The minimum number of edges in a path in G from vertex 1 to vertex 100 is</p>
<ol style="list-style-type: upper-alpha;">
<li>4</li>
<li>7</li>
<li>23</li>
<li>99</li>
</ol>Graph Theoryhttp://gateoverflow.in/3817/gate2005-it-56Tue, 04 Nov 2014 03:06:29 +0000GATE2004-IT-37
http://gateoverflow.in/3680/gate2004-it-37
<p>What is the number of vertices in an undirected connected graph with 27 edges, 6 vertices of degree 2, 3 vertices of degree 4 and remaining of degree 3?</p>
<ol style="list-style-type: upper-alpha;">
<li>10</li>
<li>11</li>
<li>18</li>
<li>19</li>
</ol>Graph Theoryhttp://gateoverflow.in/3680/gate2004-it-37Sun, 02 Nov 2014 09:32:47 +0000