What is the maximal number of edges of a graph with n vertices and k components?

Hence the maximum is achieved when only one of the components has more than one vertex. How many vertices does this graph have? the big component has n−k+1 vertices and is the only one with edges. So it has (n−k+1)(n−k)2 edges.

How many edges does a forest with n vertices and k connected components have?

If G is a forest with n vertices and k connected components, how many edges does G have? Explanation: Each component will have n/k vertices (pigeonhole principle). Hence, for each component there will be (n/k)-1 edges.

What is the maximum number of edges in a graph on n vertices with no triangle?

The basic statement of extremal graph theory is Mantel’s theorem, proved in 1907, which states that any graph on n vertices with no triangle contains at most n2/4 edges.

Which of the following have maximum number of edges?

Hence, option (c) Cuboid is the correct answer.

What is the maximum number of edges in a simple graph with 11 vertices and 3 components?

Therefor, there are total 28 edges maximum.

How many edges are there in a forest with P components having n vertices in all?

In a tree with n vertices, there are exactly n−1 edges.

What is the maximum number of edges in a spanning tree with n vertices?

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. A complete graph can have maximum nn-2 number of spanning trees.

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

Discussion Forum

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

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. Show activity on this post. 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 maximum number of edges in a graph with 8 vertices?

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

How to find the maximum number of edges in an undirected graph?

Now for example, if we are making an undirected graph with n=2 (4 vertices) and there are 2 connected components i.e, k=2, then first connected component contains either 3 vertices or 2 vertices, for simplicity we take 3 vertices (Because connected component containing 2 vertices each will not results in maximum number of edges).

How many edges possible in a bipartite graph of n vertices?

Given an integer N which represents the number of Vertices. The Task is to find the maximum number of edges possible in a Bipartite graph of N vertices. A Bipartite graph is one which is having 2 sets of vertices.

How do you increase the number of edges in a graph?

Suppose there were two strongly connected components having m and n vertices where m < n. Now if you remove a vertex from the one having m vertices and add it to the other component, then effectively you have removed m − 1 edges from the first graph and added n edges to the second graph. So, there is a net gain in the number of edges.

How do you find the maximum number of vertices a component can have?

A component should have at least 1 vertex, so give 1 vertex to the k-1 components. Now n- (k-1) = n-k+1 vertices remain. For the maximum edges, this large component should be complete. Maximum edges possible with n-k+1 vertex = ( n − k + 1 2) = ( n − k + 1) ( n − k) 2