What is the number of edges in the complete graph of vertices N?

A complete graph has an edge between any two vertices. You can get an edge by picking any two vertices. So if there are n vertices, there are n choose 2 = (n2)=n(n−1)/2 edges.

What is the maximum number of edges or lines that can be drawn for a 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.

How many edges are in a connected graph?

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 edges are there in a complete graph with 8 vertices?

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

How many edges does a fully connected graph with N nodes have?

So a complete graph on n vertices contains n(n – 1)/2 edges and your question is equivalent to asking what value of n makes n(n – 1)/2 = 45. 10 x 9/2 = 45 so the answer is 10. If you pick any two vertices, there will be an edge between them (and a different edge for each pair.)

What is edges and vertices in graph?

A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges. The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science.

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.

What is the maximum degree of any vertex in simple graph with n vertices?

n − 1
11.1. 20 – In a graph with n vertices, the highest degree possible is n − 1 since there are only n − 1 edges for any particular vertex to be adjacent to. Therefore, in a graph with 5 vertices, no vertex could have degree 5.

What is the maximum number of edges?

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. If the graph is not a multi graph then it is clearly n * (n – 1), as each node can at most have edges to every other node.

What is the minimum number of edges in a connected graph with n vertices?

n-1
The minimum number of edges in a connected graph with n vertex is n-1 i.e. Tree.

How many edges are there in complete graph with 6 vertices?

For 3 vertices the maximum number of edges is 3; for 4 it is 6; for 5 it is 10 and for 6 it is 15.

What is the maximum number of edges present in a simple directed graph?

Discussion Forum

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

A connected graph with m edges can have at most m + 1 vertices. Connected graphs with m edges and m + 1 vertices are necessarily trees. The maximum number of vertices in a connected graph with 17 edges is 18. so number of vertices is 6.

Which graph has the maximum number of edges?

A complete graph has the maximum number of edges, which is given by n choose 2 = n* (n-1)/2. Show activity on this post. Can also be thought of as the number of ways of choosing pairs of nodes n choose 2 = n (n-1)/2.

What is the total number of edges with n vertices?

Therefore, the total should be (n – k + 1) (n – k) / 2. Hope this helps! Show activity on this post. It is because maximum number of edges with n vertices is n (n-1)/2.

How many directed edges can an undirected graph have?

This is intuitive in the sense that, you are basically choosing 2 vertices from a collection of n vertices. This is the maximum number of edges an undirected graph can have. Now, for directed graph, each edge converts into two directed edges.