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

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

The maximum number of edges in an undirected graph is n(n-1)/2 and obviously in a directed graph there are twice as many.

**What is the maximum number of edges or lines that can be drawn for a simple graph with 10 vertices?**

The total number of lines that can be drawn is C (10, 2) = 45. In other words, there are all together 45 ways to choose 2 different vertices out of the given 10 vertices. The handshaking theorem states that the sum of the degrees of an undirected graph is ___ the number of edges of the graph.

**What is the maximum possible number of edges in a simple graph on 6 vertices?**

For example in a simple graph with 6 vertices, there can be at most 15 edges. If there were any more edges then 2 edges would connect the same pair of vertices and thus would not be a simple graph.

### What is the maximum number of edges possible in a simple planar graph with?

In fact, a planar graph G is a maximal planar graph if and only if each face is of length three in any planar embedding of G. Corollary 1.8. 2: The number of edges in a maximal planar graph is 3n-6.

**What is the maximum number of edges present in a simple directed graph with 7 vertices if there exists no cycles in the graph describe?**

Discussion Forum

Que. | What is the maximum number of edges present in a simple directed graph with 7 vertices if there exists no cycles in the graph? |
---|---|

b. | 7 |

c. | 6 |

d. | 49 |

Answer:6 |

**What is the maximum number of edges on a simple disconnected graph with n vertices Why?**

The maximum number of edges in a graph with N vertices is NC2 (link). Note that, to remain unconnected, one of the vertices should not have any edges. More formally, there has to be a cut (across which there won’t be any edges) with one side having only one vertex.

## What is the maximum number of edges in a simple graph with 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 maximum number of edges for a simple graph with 9 vertices?**

A simple graph with n vertices and k components has at most (n-k)*(n-k+1)/2 edges. So the given graph can have at most (9-2)*(9-2+1)/2=28 edges under the assumption that it is a simple graph.

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

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

### What is the maximum number of edges possible in a simple planar graph with 4?

If the graph must be connected, the minimum number of edges would be 4. If the graph need not be simple, then there is no maximum number of edges. If the graph must be simple, then the maximum number of edges would be 9, since K5 is not planar, but K5−e is.

**What is the maximum number of edges in a bipartite graph on 14 vertices?**

49

Explanation: By definition, the maximum possible number of edges in a bipartite graph on ‘n’ vertices = (1/4) x n2. ∴ Maximum number of edges in a bipartite graph on 14 vertices = 49.

**What is the maximum number of edges in a simple graph with 7 vertices?**