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

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

(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.

## What is the minimum number of edges in a strongly connected graph on n vertices?

The minimum number is n, because you can create a cycle with them that connects all the n vertices in one strongly-connected component.

How many maximum edges does the graph have with N nodes?

If you have N nodes, there are N – 1 directed edges than can lead from it (going to every other node). Therefore, the maximum number of edges is N * (N – 1) .

### How do I prove that the minimum number of edges in a connected graph with n vertices is n 1 )?

Proof: We know that the minimum number of edges required to make a graph of n vertices connected is (n-1) edges. We can observe that removal of one edge from the graph G will make it disconnected. Thus a connected graph of n vertices and (n-1) edges cannot have a circuit. Hence a graph G is a tree.

### What is the minimum and maximum number of edges in a simple graph of n vertices?

A graph with no loops and no parallel edges is called a simple graph. The maximum number of edges possible in a single graph with ‘n’ vertices is nC2 where nC2 = n(n – 1)/2.

What is the minimum number of edges in a cycle?

In a directedndirected graph that is not simple, you can have a cycle formed with two edges between two vertices, and even a single edge cycle formed by an edge from a vertex to itself (also called a “loop”).

## What is the minimum number of edges in a connected graph having 15 vertices?

2 Answers. The minimum number of edges for undirected connected graph is (n-1) edges.

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

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

What is the minimum number of spanning tree in a connected graph?

Every undirected and connected graph has a minimum of one spanning tree.

### 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.

### What is the minimum number of edges on a strongly connected Diagraph with n vertices explain with proper justification?

Given a Directed graph of N vertices and M edges, the task is to find the minimum number of edges required to make the given graph Strongly Connected. Explanation: 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.