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Recent questions tagged graph-theory

0 votes
1 answer
1
UGCNET-Oct2020-II: 26
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 $j$ if and only if either $j=i+1$ or $j=3i$. The minimum number of edges in a path in $G$ from vertex $1$ to vertex $100$ is ______ $23$ $99$ $4$ $7$
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 $j$ if and only if either $j=i+1$ or $j=3i$. The minimum number of edges in a path in $G$ from vertex $1$ to vertex $100$ is ______ $23$ $99$ $4$ $7$
asked Nov 20, 2020 in Discrete Mathematics jothee 77 views
0 votes
1 answer
2
UGCNET-Oct2020-II: 53
Consider the following statements: Any tree is $2$-colorable A graph $G$ has no cycles of even length if it is bipartite A graph $G$ is $2$-colorable if is bipartite A graph $G$ can be colored with $d+1$ colors if $d$ is the maximum degree of any vertex in the graph ... $(b)$ and $(c)$ are incorrect $(b)$ and $(e)$ are incorrect $(a)$ and $(d)$ are incorrect
Consider the following statements: Any tree is $2$-colorable A graph $G$ has no cycles of even length if it is bipartite A graph $G$ is $2$-colorable if is bipartite A graph $G$ can be colored with $d+1$ colors if $d$ is the maximum degree of any vertex in the graph $G$ ... and $(e)$ are incorrect $(b)$ and $(c)$ are incorrect $(b)$ and $(e)$ are incorrect $(a)$ and $(d)$ are incorrect
asked Nov 20, 2020 in Discrete Mathematics jothee 35 views
0 votes
0 answers
3
UGCNET-Oct2020-II: 86
Let $G$ be a simple undirected graph, $T_D$ be a DFS tree on $G$, and $T_B$ be the BFS tree on $G$. Consider the following statements. Statement $I$: No edge of $G$ is a cross with respect to $T_D$ Statement $II$ ... $I$ and Statement $II$ are false Statement $I$ is correct but Statement $II$ is false Statement $I$ is incorrect but Statement $II$ is true
Let $G$ be a simple undirected graph, $T_D$ be a DFS tree on $G$, and $T_B$ be the BFS tree on $G$. Consider the following statements. Statement $I$: No edge of $G$ is a cross with respect to $T_D$ Statement $II$: For every edge $(u,v)$ of $G$ ... Statement $I$ and Statement $II$ are false Statement $I$ is correct but Statement $II$ is false Statement $I$ is incorrect but Statement $II$ is true
asked Nov 20, 2020 in Discrete Mathematics jothee 33 views
3 votes
3 answers
6
NIELIT 2017 DEC Scientific Assistant A - Section B: 20
Total number of simple graphs that can be drawn using six vertices are: $2^{15}$ $2^{14}$ $2^{13}$ $2^{12}$
Total number of simple graphs that can be drawn using six vertices are: $2^{15}$ $2^{14}$ $2^{13}$ $2^{12}$
asked Mar 31, 2020 in Graph Theory Lakshman Patel RJIT 556 views
1 vote
1 answer
7
NIELIT 2017 DEC Scientific Assistant A - Section B: 38
If a planner graph, having $25$ vertices divides the plane into $17$ different regions. Then how many edges are used to connect the vertices in this graph. $20$ $30$ $40$ $50$
If a planner graph, having $25$ vertices divides the plane into $17$ different regions. Then how many edges are used to connect the vertices in this graph. $20$ $30$ $40$ $50$
asked Mar 31, 2020 in Graph Theory Lakshman Patel RJIT 219 views
0 votes
2 answers
8
NIELIT 2016 MAR Scientist B - Section B: 1
The number of ways to cut a six sided convex polygon whose vertices are labeled into four triangles using diagonal lines that do not cross is $13$ $14$ $12$ $11$
The number of ways to cut a six sided convex polygon whose vertices are labeled into four triangles using diagonal lines that do not cross is $13$ $14$ $12$ $11$
asked Mar 31, 2020 in Graph Theory Lakshman Patel RJIT 395 views
1 vote
1 answer
10
NIELIT 2016 DEC Scientist B (CS) - Section B: 5
Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to: $3$ $4$ $5$ $6$
Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to: $3$ $4$ $5$ $6$
asked Mar 31, 2020 in Graph Theory Lakshman Patel RJIT 204 views
0 votes
1 answer
11
NIELIT 2017 July Scientist B (IT) - Section B: 1
Given an undirected graph $G$ with $V$ vertices and $E$ edges, the sum of the degrees of all vertices is $E$ $2E$ $V$ $2V$
Given an undirected graph $G$ with $V$ vertices and $E$ edges, the sum of the degrees of all vertices is $E$ $2E$ $V$ $2V$
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 1.8k views
0 votes
2 answers
12
NIELIT 2017 July Scientist B (IT) - Section B: 2
Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? In adjacency list representation, space is saved for sparse graphs. Deleting a vertex in adjacency list ... Adding a vertex in adjacency list representation is easier than adjacency matrix representation. All of the option.
Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? In adjacency list representation, space is saved for sparse graphs. Deleting a vertex in adjacency list representation is easier than ... matrix representation. Adding a vertex in adjacency list representation is easier than adjacency matrix representation. All of the option.
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 1.4k views
0 votes
1 answer
13
NIELIT 2017 July Scientist B (IT) - Section B: 3
A path in graph $G$, which contains every vertex of $G$ and only once? Euler circuit Hamiltonian path Euler Path Hamiltonian Circuit
A path in graph $G$, which contains every vertex of $G$ and only once? Euler circuit Hamiltonian path Euler Path Hamiltonian Circuit
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 360 views
0 votes
1 answer
14
NIELIT 2017 July Scientist B (IT) - Section B: 5
In a given following graph among the following sequences: abeghf abfehg abfhge afghbe Which are depth first traversals of the above graph? I,II and IV only I and IV only II,III and IV only I,III and IV only
In a given following graph among the following sequences: abeghf abfehg abfhge afghbe Which are depth first traversals of the above graph? I,II and IV only I and IV only II,III and IV only I,III and IV only
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 204 views
0 votes
1 answer
15
NIELIT 2017 July Scientist B (IT) - Section B: 6
Considering the following graph, which one of the following set of edged represents all the bridges of the given graph? $(a,b), (e,f)$ $(a,b), (a,c)$ $(c,d), (d,h)$ $(a,b)$
Considering the following graph, which one of the following set of edged represents all the bridges of the given graph? $(a,b), (e,f)$ $(a,b), (a,c)$ $(c,d), (d,h)$ $(a,b)$
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 154 views
0 votes
1 answer
16
NIELIT 2017 July Scientist B (IT) - Section B: 7
Which of the following statements is/are TRUE? $S1$:The existence of an Euler circuit implies that an Euler path exists. $S2$:The existence of an Euler path implies that an Euler circuit exists. $S1$ is true. $S2$ is true. $S1$ and $S2$ both are true. $S1$ and $S2$ both are false.
Which of the following statements is/are TRUE? $S1$:The existence of an Euler circuit implies that an Euler path exists. $S2$:The existence of an Euler path implies that an Euler circuit exists. $S1$ is true. $S2$ is true. $S1$ and $S2$ both are true. $S1$ and $S2$ both are false.
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 216 views
0 votes
1 answer
17
NIELIT 2017 July Scientist B (IT) - Section B: 8
A connected planar graph divides the plane into a number of regions. If the graph has eight vertices and these are linked by $13$ edges, then the number of regions is: $5$ $6$ $7$ $8$
A connected planar graph divides the plane into a number of regions. If the graph has eight vertices and these are linked by $13$ edges, then the number of regions is: $5$ $6$ $7$ $8$
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 220 views
0 votes
1 answer
18
NIELIT 2017 July Scientist B (IT) - Section B: 12
Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is $6$ $8$ $9$ $13$
Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is $6$ $8$ $9$ $13$
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 121 views
0 votes
1 answer
19
NIELIT 2017 July Scientist B (IT) - Section B: 15
The number of diagonals that can be drawn by joining the vertices of an octagon is $28$ $48$ $20$ None of the option
The number of diagonals that can be drawn by joining the vertices of an octagon is $28$ $48$ $20$ None of the option
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 134 views
0 votes
1 answer
20
NIELIT 2017 July Scientist B (CS) - Section B: 2
Which of the following statements is/are TRUE for an undirected graph? Number of odd degree vertices is even Sum of degrees of all vertices is even P only Q only Both P and Q Neither P nor Q
Which of the following statements is/are TRUE for an undirected graph? Number of odd degree vertices is even Sum of degrees of all vertices is even P only Q only Both P and Q Neither P nor Q
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 322 views
0 votes
4 answers
21
NIELIT 2017 July Scientist B (CS) - Section B: 11
Consider the following graph $L$ and find the bridges,if any. No bridge $\{d,e\}$ $\{c,d\}$ $\{c,d\}$ and $\{c,f\}$
Consider the following graph $L$ and find the bridges,if any. No bridge $\{d,e\}$ $\{c,d\}$ $\{c,d\}$ and $\{c,f\}$
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 359 views
0 votes
3 answers
22
NIELIT 2017 July Scientist B (CS) - Section B: 12
The following graph has no Euler circuit because It has $7$ vertices. It is even-valent (all vertices have even valence). It is not connected. It does not have a Euler circuit.
The following graph has no Euler circuit because It has $7$ vertices. It is even-valent (all vertices have even valence). It is not connected. It does not have a Euler circuit.
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 568 views
0 votes
7 answers
23
NIELIT 2017 July Scientist B (CS) - Section B: 13
For the graph shown, which of the following paths is a Hamilton circuit? $ABCDCFDEFAEA$ $AEDCBAF$ $AEFDCBA$ $AFCDEBA$
For the graph shown, which of the following paths is a Hamilton circuit? $ABCDCFDEFAEA$ $AEDCBAF$ $AEFDCBA$ $AFCDEBA$
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 592 views
0 votes
4 answers
24
NIELIT 2017 July Scientist B (CS) - Section B: 14
If $G$ is an undirected planar graph on $n$ vertices with $e$ edges then $e\leq n$ $e\leq 2n$ $e\leq 3n$ None of the option
If $G$ is an undirected planar graph on $n$ vertices with $e$ edges then $e\leq n$ $e\leq 2n$ $e\leq 3n$ None of the option
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 1.4k views
0 votes
2 answers
25
NIELIT 2017 July Scientist B (CS) - Section B: 15
Choose the most appropriate definition of plane graph. A simple graph which is isomorphic to hamiltonian graph. A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non-empty disjoint subset $X$ and ... in a plane in such a way that any pair of edges meet only at their end vertices. None of the option.
Choose the most appropriate definition of plane graph. A simple graph which is isomorphic to hamiltonian graph. A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non-empty disjoint subset $X$ and $Y$ in such a way that each edge ... . A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices. None of the option.
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 546 views
0 votes
1 answer
26
NIELIT 2017 DEC Scientist B - Section B: 23
Let $G$ be a complete undirected graph on $8$ vertices. If vertices of $G$ are labelled, then the number of distinct cycles of length $5$ in $G$ is equal to: $15$ $30$ $56$ $60$
Let $G$ be a complete undirected graph on $8$ vertices. If vertices of $G$ are labelled, then the number of distinct cycles of length $5$ in $G$ is equal to: $15$ $30$ $56$ $60$
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 567 views
1 vote
4 answers
27
NIELIT 2017 DEC Scientist B - Section B: 52
Let $G$ be a simple undirected graph on $n=3x$ vertices $(x \geq 1)$ with chromatic number $3$, then maximum number of edges in $G$ is $n(n-1)/2$ $n^{n-2}$ $nx$ $n$
Let $G$ be a simple undirected graph on $n=3x$ vertices $(x \geq 1)$ with chromatic number $3$, then maximum number of edges in $G$ is $n(n-1)/2$ $n^{n-2}$ $nx$ $n$
asked Mar 30, 2020 in Graph Theory Lakshman Patel RJIT 926 views
0 votes
1 answer
28
UGCNET-Jan2017-II: 5
Consider a Hamiltonian Graph $G$ with no loops or parallel edges and with $\left | V\left ( G \right ) \right |= n\geq 3$. The which of the following is true? $\text{deg}\left ( v \right )\geq \frac{n}{2}$ for each vertex $v\\$ ... $v$ and $w$ are not connected by an edge All of the above
Consider a Hamiltonian Graph $G$ with no loops or parallel edges and with $\left | V\left ( G \right ) \right |= n\geq 3$. The which of the following is true? $\text{deg}\left ( v \right )\geq \frac{n}{2}$ for each vertex $v\\$ ... $v$ and $w$ are not connected by an edge All of the above
asked Mar 24, 2020 in Graph Theory jothee 214 views
6 votes
3 answers
29
GATE 2020 CSE | Question: 52
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is _______
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is _______
asked Feb 12, 2020 in Graph Theory Arjun 3.2k views
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