# What is the maximum number of edges in a connected graph?

## What is the maximum number of edges in a connected graph?

A complete graph has the maximum number of edges, which is given by n choose 2 = n*(n-1)/2.

## What is the maximum number of edges in a graph with n vertices?

n – 1 edges

For maximum number of edges each vertex connect to other vertex only if it does not from a cycle i.e. from a tree with n vertices, which has maximum n – 1 edges.

What is the maximum number of edges in a graph with 10 vertices?

What is the maximum number of edges in a bipartite graph having 10 vertices? Explanation: Let one set have n vertices another set would contain 10-n vertices. Total number of edges would be n*(10-n), differentiating with respect to n, would yield the answer. 11.

What’s the maximum number of edges a graph on 8 vertices can have?

Therefore a simple graph with 8 vertices can have a maximum of 28 edges.

### What is the total number of graphs possible with n vertices?

The maximum number of edges a graph with N vertices can contain is X = N * (N – 1) / 2. Hence, the total number of graphs that can be formed with n vertices will be: C0 + XC1 + XC2 + … + XCX = 2X.

### What is the largest number of edges possible in a graph with 12 vertices?

19 edges
We can have a graph with 12 vertices and 19 edges (draw an example) and so this must be the maximum number of vertices possible.

What is the maximum possible number of edges?

=nk=1, and the maximum number of edges is (n−k+12).

How many edges are there in a complete graph with 5 vertices?

ten edges
It has ten edges which form five crossings if drawn as sides and diagonals of a convex pentagon. The four thick edges connect the same five vertices and form a spanning tree of the complete graph.

#### How many edges are there in a graph with n vertices each of degree 6?

Example: How many edges are there in a graph with 10 vertices, each of degree 6? Solution: The sum of the degrees of the vertices is 610 = 60. According to the Handshaking Theorem, it follows that 2e = 60, so there are 30 edges.

#### What is the maximum number of edges for an undirected graph of 10 vertices?

Hence the correct answer is 36.

Can there be a graph with 8 vertices and 29 edges?

8(8-1) / 2 = 28. Therefore a simple graph with 8 vertices can have a maximum of 28 edges.

How many edges must be removed from a connected graph?

m−n+1 edges need to be removed.

## How many regions does a connected graph with 10 vertices and 12 edges have?

Solution. Hence, the number of regions is 12.

## What is the maximum number of edges in an undirected graph with n?

What is the maximum number of edges in an acyclic undirected graph with n vertices? Explanation: n * (n – 1) / 2 when cyclic.

Can a simple graph have 6 vertices and 17 edges?

Take 1 vertex with 17 loops, or two vertices with 17 edges between them, and let the other vertices be isolated. Now assuming we are working with a simple graph (no loops, and no multiple edges), then no such graph exists. This is because the maximum number of edges that can exist on a simple graph of 6 vertices is 15.

What is the minimum number of edges which must be removed?

Removing any one of the edges will make the graph acyclic. Therefore, at least one edge needs to be removed.

### How many edges must be removed from a connected graph with 5 vertices and 6 edges to produce a spanning tree?

Spanning tree has n-1 edges, where n is the number of nodes (vertices). From a complete graph, by removing maximum e – n + 1 edges, we can construct a spanning tree.

### How many region does a connected planar graph with n vertices and 12 edges have?

Since G is planar we can use Euler’s Identity, n−m+r=2, where n=6 and m=12. Thus 6−12+r=2 implies that r=8. By The First Theorem of Graph Theory the sum of all the degrees in G is 2m=2(12)=24. Since the number of regions is r=8 we know that each region is bounded by 24/8=3 edges.

How many edges are there in a connected planar graph having 6 vertices and 8 regions?

Solution Having six vertices each of degree 4, thanks to the handshaking theorem we get that the number of edges is: 12 By using Euler formula we get T = e-V+2 T =42 – 6+2 = 8.

What is the minimum number of edges in an undirected graph with n vertices?

(n-1)
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.

#### Can an 6 4 )- graph is connected?

Yes. If a graph has a spanning path, then it is possible to go from any vertex to any other vertex by edges of the graph. Hence the graph is connected.

#### What is the minimum possible number of edges in a directed graph?

Adding a directed edge joining the pair of vertices {3, 1} makes the graph strongly connected. Hence, the minimum number of edges required is 1.

How many edges must be removed from a connected graph with n vertices?

\$m-n+1\$ edges need to be removed.

How many regions does a connected planar graph with 10 vertices and 12 edges?