## 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 610 = 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?**