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.

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

A connected 10-vertex graph can have as few as 9 (if it is just a broken line) and as many as 10*9/2=45 (if it is a complete decagon) edges.

What is the maximum possible number of edges in a directed acyclic graph with 2n vertices?

Therefore each node than can have n-1 edges adjacent on it and so the maximum number of edges in the graph is n(n−1)/2.

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

If you add them to your graph, you get a simple graph, which by handshaking lemma, has at most n(n−1)2 edges. Therefore, your graph has at most n(n−1)2−k(n−k) edges, with equality if the two pieces are complete graphs. To maximize this number, you need to minimize k(n−k) when 1≤k≤n−1.

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.

What is maximum edge of a triangle?

For , the number of edges is one. Hence the maximum number of edges in a planar triangle-free graph on vertices is zero if , one if , and if .

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

Therefor, there are total 28 edges maximum.

What is the maximum number of edges in a simple disconnected graph with n vertices?

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 many maximum edges includes in simple graph with 5 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 degree of a complete graph with n vertices?

If you mean a simple graph, with at most one edge connecting two vertices, then the maximum degree is n − 1. A complete graph with n vertices is a simple graph where every vertex has degree n − 1, that is, each vertex is (directly) connected with every other vertex with an edge. In this case the number of edges is

What is the maximum number of edges a graph can have?

The maximum number of edges is simply the number of pairs of distinct vertices; if there are n vertices, this is ( n 2) = n! 2! ( n − 2)! = n ( n − 1) 2. Thanks for contributing an answer to Mathematics Stack Exchange!

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.

What is the value of n(n-1) for an undirected graph?

For a regular graph you can have at most one edge between any two vertices, so you get n (n-1)/2 for an undirected graph and n (n-1) for a directed graph.