What is the minimum number of edges in an acyclic undirected graph with n vertices?
n-1
2 Answers. Yes.. 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.
What is the maximum number of edges in an undirected graph with n vertices in which each vertex has degree at most K?
So the maximum number of edges in this case are 3. This implies that replacing n with n-k+1 in the formula for maximum number of edges i.e, n(n-1)/2 will results in (n-k+1)(n-k)/2 which is maximum number of edges that a graph of n vertices with k connected component can have.
What is the maximum number of edges in a directed acyclic graph?
The maximum number of edges in a DAG with n vertices is Θ(n2). Take the complete bipartite graph Kn,n and direct all edges from left to right. This is a DAG with 2n vertices and n2 edges.
What can be the maximum number of edges in a connected graph having n vertices?
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 Gate 2004?
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 maximum number of edges in an undirected graph with n vertices Mcq?
Solution: In an undirected graph, there can be maximum n(n-1)/2 edges. We can choose to have (or not have) any of the n(n-1)/2 edges. So, total number of undirected graphs with n vertices is 2(n(n-1)/2).
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 maximum number of edges in the maximum matching of a bipartite graph with n vertices?
Prove that for a bipartite graph G on n vertices the number of edges in G is at most n24.
What is the maximum number of edges in a directed graph having 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 number of edges possible in a directed acyclic graph with 4 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.
Is the maximum number of edges in an acyclic undirected graph with k vertices Mcq?
______ is the maximum number of edges in an acyclic undirected graph with k vertices. Explanation: This is possible with spanning trees since, a spanning tree with k nodes has k – 1 edges. Explanation: For making a cyclic graph, the minimum number of edges have to be equal to the number of vertices.
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).
What is the maximum number of edges in an acyclic graph?
An acyclic undirected graph is another name for a tree. The maximum number of edges is v − 1 in a tree with v vertexes. Hiring CS majors for internships and entry-level roles. Get matched with your dream job. Start interviewing for jobs and internships with top companies. n * (n – 1) / 2 when cyclic.
How do you make a graph acyclic with n nodes?
Given an undirected graph consisting of N nodes containing values from the range [1, N] and M edges in a matrix Edges [] [], the task is to determine the minimum number of edges required to be removed such that the resulting graph does not contain any cycle. Removing any one of the edges will make the graph acyclic.
What is the maximum number of edges between three vertices?
These 3 vertices must be connected so maximum number of edges between these 3 vertices are 3 i.e, (1->2->3->1) and the second connected component contains only 1 vertex which has no edge. So the maximum number of edges in this case are 3.