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Recent questions and answers in Graph Theory

37 votes
5 answers
1
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $
answered 15 hours ago in Graph Theory varunrajarathnam 6.2k views
1 vote
4 answers
2
4 votes
2 answers
3
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. Let G be a simple graph on 8 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of ... 6 and a vertex of degree 7. Which of the following can be the degree of the last vertex? (A) 3 (B) 0 (C) 5 (D) 4
answered Oct 14 in Graph Theory ayush.5 201 views
1 vote
2 answers
7
Consider a graph $G$ with $2^{n}$ vertices where the level of each vertex is a $n$ bit binary string represented as $a_{0},a_{1},a_{2},.............,a_{n-1}$, where each $a_{i}$ is $0$ or $1$ ... $x$ and $y$ denote the degree of a vertex $G$ and number of connected component of $G$ for $n=8.$ The value of $x+10y$ is_____________
answered Oct 13 in Graph Theory arun yadav 287 views
21 votes
3 answers
8
6 votes
3 answers
9
23 votes
6 answers
11
How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$
answered Sep 26 in Graph Theory manish_pal_sunny 1.8k views
25 votes
4 answers
12
7 votes
5 answers
14
How many edges are there in a forest with $v$ vertices and $k$ components? $(v+1) - k$ $(v+1)/2 - k$ $v - k$ $v + k$
answered Sep 18 in Graph Theory Dhruvil 2.7k views
0 votes
2 answers
15
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.
answered Sep 18 in Graph Theory Dhruvil 163 views
8 votes
3 answers
16
29 votes
4 answers
17
The minimum number of colours required to colour the vertices of a cycle with $n$ nodes in such a way that no two adjacent nodes have the same colour is $2$ $3$ $4$ $n-2 \left \lfloor \frac{n}{2} \right \rfloor+2$
answered Sep 14 in Graph Theory Nishisahu 4.9k views
1 vote
1 answer
20
0 votes
2 answers
21
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 in Graph Theory Lakshman Patel RJIT 140 views
1 vote
1 answer
23
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 in Graph Theory Lakshman Patel RJIT 106 views
0 votes
1 answer
25
0 votes
1 answer
26
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 in Graph Theory Lakshman Patel RJIT 114 views
0 votes
1 answer
27
0 votes
1 answer
28
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 in Graph Theory Lakshman Patel RJIT 103 views
0 votes
1 answer
29
0 votes
1 answer
30
0 votes
1 answer
32
0 votes
3 answers
34
0 votes
7 answers
35
0 votes
2 answers
37
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 in Graph Theory Lakshman Patel RJIT 238 views
0 votes
1 answer
38
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 in Graph Theory Lakshman Patel RJIT 247 views
0 votes
1 answer
39
The number of edges in a complete graph with $‘n’$ vertices is equal to : $n(n-1)$ $\large\frac{n(n-1)}{2}$ $n^2$ $2n-1$
asked Mar 28 in Graph Theory jothee 81 views
0 votes
2 answers
40
The number of edges in a complete graph with $N$ vertices is equal to : $N (N−1)$ $2N−1$ $N−1$ $N(N−1)/2$
asked Mar 27 in Graph Theory jothee 151 views
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