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

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.

What is the minimum number of edges that must be present in a connected graph with 100 vertices such that none of the 100 vertices are cut vertices?

Explanation: Since there are 100 vertices, there must be 99 edges in Minimum Spanning Tree (MST).

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

ni −k). Theorem 4. A simple graph with n vertices and k components can have at most have (n−k)(n− k+1)/2 edges.

How many edges does a graph have with n nodes?

12 Answers If you have N nodes, there are N – 1 directed edges than can lead from it (going to every other node). Therefore, the maximum number of edges is N * (N – 1) .

What is the minimum and maximum number of edges in a simple graph of 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 in an acyclic undirected graph with n vertices?

n-1 edges
What is the maximum number of edges in an acyclic undirected graph with n vertices? Explanation: n * (n – 1) / 2 when cyclic. But acyclic graph with the maximum number of edges is actually a spanning tree and therefore, correct answer is n-1 edges.

What is the largest number of vertices in a graph with 35 edges?

What is the largest number of vertices in a graph with 35 edges if all vertices are of degree at least 3? I thought up of a solution but there are some questions I could not find. So the largest number of vertices are 23, with the given constraints.

What is the maximum number of edges of an n vertex graph that is not connected?

What will be the number of edges in a complete graph consisting of 2 nodes?

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 in a graph with 5 vertices?

ANSWER: In a simple graph, no pair of vertices can have more than one edge between them. The maximum number of edges in the complete graph containing 5 vertices is given by K5: which is C(5, 2) edges = “5 choose 2” edges = 10 edges. Since 12 > 10, it is not possible to have a simple graph with more than 10 edges.

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

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.

How many edges are in a complete graph with n vertices?