How do you find the maximum weight of a minimum spanning tree?
Table of Contents
- 1 How do you find the maximum weight of a minimum spanning tree?
- 2 Can the maximum weight edge in minimum spanning tree?
- 3 What is the weight of a minimum spanning tree of the following graph Gate 2003?
- 4 What is a minimum weight spanning tree?
- 5 How many distinct minimum spanning trees are there?
- 6 How many minimum spanning tree is possible for a graph?
How do you find the maximum weight of a minimum spanning tree?
First take a complete graph with 4 vertices with edge weights (1,2,3,4,5,6) such that (1,2,3) and (4,5,6) forms a cycle. So that we can get maximum MST. This maximum MST has weight=1+2+4=7.
How do you calculate the weight of a spanning tree?
The weight of a spanning tree is the sum of weights given to each edge of the spanning tree. How many edges does a minimum spanning tree has? A minimum spanning tree has (V – 1) edges where V is the number of vertices in the given graph.
Can the maximum weight edge in minimum spanning tree?
Does a MST contain the maximum weight edge? Sometimes, Yes. It depends on the type of graph. If the edge with maximum weight is the only bridge that connects the components of a graph, then that edge must also be present in the MST.
How do you find the maximum number of spanning trees?
If a graph is a complete graph with n vertices, then total number of spanning trees is n(n-2) where n is the number of nodes in the graph. In complete graph, the task is equal to counting different labeled trees with n nodes for which have Cayley’s formula.
What is the weight of a minimum spanning tree of the following graph Gate 2003?
The graph shown below 8 edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight 36 and contains the edges: {(A, C), (B, C), (B, E), (E, F), (D, F)}….Minimum-Spanning-Tree.
| A | (a—b),(d—f),(b—f),(d—c),(d—e) |
|---|---|
| B | (a—b),(d—f),(d—c),(b—f),(d—e) |
| C | (d—f),(a—b),(d—c),(b—f),(d—e) |
| D | (d—f),(a—b),(b—f),(d—e),(d—c) |
Which is the maximum number of possible spanning tree from the following graph?
nn-2
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 a minimum weight spanning tree?
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. There are many use cases for minimum spanning trees.
What is a MIN MAX spanning tree?
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.
How many distinct minimum spanning trees are there?
Minimum spanning tree will have weight 11, hence 6 is the correct answer.
Which of the following can be used to efficiently implement Prim’s algorithm for graphs?
Explanation: Prim’s algorithm can be implemented using Fibonacci heap and it never accepts cycles.
How many minimum spanning tree is possible for a graph?
one minimum spanning tree
There is only one minimum spanning tree in the graph where the weights of vertices are different.