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What is the maximum number of distinct edges in an undirected graph with N vertices?
Wiki User
∙ 11y ago
Let G be a complete graph with n vertices. Consider the case where n=2. With only 2 vertices it is clear that there will only be one edge. Now add one more vertex to get n = 3. We must now add edges between the two old vertices and the new one for a total of 3 vertices. We see that adding a vertex to a graph with n vertices gives us n more edges. We get the following sequence
Edges on a graph with n vertices: 0+1+2+3+4+5+...+n-1. Adding this to itself and dividing by two yields the following formula for the number of edges on a complete graph with n vertices: n(n-1)/2.
Wiki User
∙ 12y ago
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Given an undirected graph G and an integer k?
Given an undirected graph G=(V,E) and an integer k, find induced subgraph H=(U,F) of G of maximum size (maximum in terms of the number of vertices) such that all vertices of H have degree at least k
A simple graph with n vertices and k components can have atmost how many edges?
In a connected component of a graph with Mi vertices, the maximum number of edges is MiC2 or Mi(Mi-1)/2. So if we have k components and each component has Mi vertices then the maximum number of edges for the graph is M1C2+M2C2+...+MKC2. Of course the sum of Mi as i goes from 1 to k must be n since the sum of the vertices in each component is the sum of all the vertices in the graph which you gave as n. Where MC2 means choose 2 from M and there are M(M-1)/2 ways to do that.
What do we know about a number that has an odd number of distinct factors?
It's a perfect square.
Does a perfect square number have even or odd number of distinct factors?
An odd number.
When does a number has 3 distinct factors?
When the number is a square of a prime number. Of course, it will have a repeated factor, but it will still only have 3 distinct factors. 4, 9, 25, 49, 121 are some examples.
What is the maximum number of edges in an undirected graph with V vertices?
V*(V-1)/2
Given an undirected graph G and an integer k?
Given an undirected graph G=(V,E) and an integer k, find induced subgraph H=(U,F) of G of maximum size (maximum in terms of the number of vertices) such that all vertices of H have degree at least k
What is the maximum number of edges in an acyclic undirected graph with n vertices?
n * (n - 1) / 2 That would ignore the "acyclic" part of the question. An acyclic graph with the maximum number of edges is a tree. The correct answer is n-1 edges.
What is the sum of degrees of all vertices in an undirected graph is twice the number of edges?
It is a true statement.
Maximum number of edges in an acyclic undirected graph with n?
n - 1
What is n in Maximum number of edges in an acyclic undirected graph with n?
n-1
What prisms have vertices?
Every prism has vertices. They have an even number of vertices, with a minimum of 6 and no maximum.
What 3d figure has 8 faces 24 edges and 16 vertices?
There is no such polyhedron. The numbers given in the question do not satisfy the Euler characteristic for simply connected polyhedra.Alternatively, the fact that it has eight faces means that is should be an octahedron. However, among the 257 topologically distinct convex octahedra, the maximum number of vertices is 12 and the maximum number of edges is 18. Both these numbers are well below what you require!
What is the maximum number of points of intersection when three distinct circles and four distinct lines?
discuss the possible number of points of interscetion of two distinct circle
What is the maximum number of intersections that two tringles with different vertices could in a coordinate plane?
Six.
What is the maximum number of points of intersection of 4 distinct lines?
Six (6)
What has 6 vertices and 15 edges?
I believe that such an object cannot exist in normal 3-d space. If there are 6 vertices, the maximum number of edges is 12.
