Table of Contents

- 1 How many vertices does a tree with 17 edges have?
- 2 How many vertices does a connected graph have?
- 3 How many Hamilton circuits are in a graph with 8 vertices?
- 4 What is the maximum number of vertices?
- 5 How many vertices are there in a graph with 16 edges if each vertex is of degree 4?
- 6 How many Hamilton circuits are in a graph with 9 vertices?
- 7 How do you find the maximum number of vertices a component can have?
- 8 How many components does a graph have that is not connected?

## How many vertices does a tree with 17 edges have?

17 edges means 34 edge-vertex incidences.

**What is the maximum number of vertices in a connected graph of n edges?**

In a directed graph having N vertices, each vertex can connect to N-1 other vertices in the graph(Assuming, no self loop). Hence, the total number of edges can be are N(N-1).

### How many vertices does a connected graph have?

A graph with just one vertex is connected. An edgeless graph with two or more vertices is disconnected. A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph.

**What is the maximum number of edges in a simple graph with 15 vertices?**

The maximum number of edges possible in a single graph with ‘n’ vertices is nC2 where nC2 = n(n – 1)/2. The number of simple graphs possible with ‘n’ vertices = 2nc2 = 2n(n-1)/2.

## How many Hamilton circuits are in a graph with 8 vertices?

5040 possible Hamiltonian circuits

A complete graph with 8 vertices would have = 5040 possible Hamiltonian circuits.

**How many vertices does a tree have?**

A labeled tree with 6 vertices and 5 edges. In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph.

### What is the maximum number of vertices?

Cuboid has the maximum number of vertices. Hence, option (c) Cuboid is the correct answer.

**How do you find the maximum number of vertices?**

We know that e1+e2+e3+e4+e5=40 so there can be 45 vertices maximum.

## How many vertices are there in a graph with 16 edges if each vertex is of degree 4?

two vertices

Answer and Explanation: Given that a graph g has 16 edges, two vertices of degree 4 , two of degree 1 and the remaining vertices…

**How many edges does a connected graph have?**

The minimum number of edges for undirected connected graph is (n-1) edges. To see this, since the graph is connected then there must be a unique path from every vertex to every other vertex and removing any edge will make the graph disconnected.

### How many Hamilton circuits are in a graph with 9 vertices?

Example16.3

Number of vertices | Number of unique Hamilton circuits |
---|---|

6 | 60 |

7 | 360 |

8 | 2520 |

9 | 20,160 |

**What is the maximum number of edges a graph can have?**

The maximum number of edges is simply the number of pairs of distinct vertices; if there are n vertices, this is ( n 2) = n! 2! ( n − 2)! = n ( n − 1) 2. Thanks for contributing an answer to Mathematics Stack Exchange!

## How do you find the maximum number of vertices a component can have?

A component should have at least 1 vertex, so give 1 vertex to the k-1 components. Now n- (k-1) = n-k+1 vertices remain. For the maximum edges, this large component should be complete. Maximum edges possible with n-k+1 vertex = ( n − k + 1 2) = ( n − k + 1) ( n − k) 2

**How do you join two components with more than one vertex?**

Then there exist two components with more than one vertex say the number of vertices are $n$ and $m$ . Pick the one with the less vertices suppose it is $m$ vertices. Take one of it vertices and delete it. removing $m-1$ edges. now add a new vertex to the component with $n$ vertices and join it to all its vertices, adding $n$ edges.

### How many components does a graph have that is not connected?

Since the graph is not connected it has at least two components. Even if it has more than 2 components, you can think about it as having 2 “pieces”, not necessarily connected. Let k and n − k be the number of vertices in the two pieces.