A spanning tree can never contain a cycle
. Spanning tree is always minimally connected i.e. if we remove one edge from the spanning tree, it will become disconnected. A spanning tree is maximally acyclic i.e. if we add one edge to the spanning tree, it will create a cycle or a loop.
What will be false in case of the minimum spanning tree?
Explanation: Every MST will contain CD as it is smallest edge. So, Every minimum spanning tree of G must contain CD is true. And G has a unique minimum spanning tree is also true because the graph has edges with distinct weights. So,
no minimum spanning tree contains AB is false
.
What are the properties of minimum spanning tree?
- Possible multiplicity. If there are n vertices in the graph, then each spanning tree has n − 1 edges.
- Uniqueness. …
- Minimum-cost subgraph. …
- Cycle property. …
- Cut property. …
- Minimum-cost edge. …
- Contraction.
What do you mean by minimum spanning tree?
The Minimum Spanning Tree is
the one whose cumulative edge weights have the smallest value
, however. Think of it as the least cost path that goes through the entire graph and touches every vertex.
How do you find the minimum spanning tree?
different labeled trees. Now to find the minimum spanning tree among all the spanning trees, we need to
calculate the total edge weight for each spanning tree
. A minimum spanning tree is a spanning tree with the smallest edge weight among all the spanning trees. corresponds to the minimum spanning tree.
Which of the following is false in the case of a minimum spanning tree of a graph G?
| Q. Which of the following is false in the case of a spanning tree of a graph G? | B. it is a subgraph of the g | C. it includes every vertex of the g | D. it can be either cyclic or acyclic | Answer» d. it can be either cyclic or acyclic |
|---|
Which of the following is not an algorithm to find the minimum spanning tree of the given graph?
| Q. Which of the following is not the algorithm to find the minimum spanning tree of the given graph? | B. prim’s algorithm | C. kruskal’s algorithm | D. bellman–ford algorithm | Answer» d. bellman–ford algorithm |
|---|
Which of the following statements about minimum spanning tree is correct?
A minimum spanning tree
must have the edge with the smallest weight
(In Kruskal’s algorithm we start from the smallest weight edge). So, C is TRUE.
Is minimum spanning tree NP complete?
The problem of finding the Steiner tree of a subset of the vertices, that is,
minimum tree that spans the given subset, is known to be NP-Complete
.
What is spanning tree and minimum spanning tree in data structure?
A spanning tree is a subset of an undirected Graph that has all the vertices connected by minimum number of edges
. If all the vertices are connected in a graph, then there exists at least one spanning tree. In a graph, there may exist more than one spanning tree.
How is spanning tree different from minimal spanning tree?
If the graph is edge-weighted, we can define the weight of a spanning tree as the sum of the weights of all its edges.
A minimum spanning tree is a spanning tree whose weight is the smallest among all possible spanning trees
.
Is Kruskal algorithm greedy?
It is a greedy algorithm in graph theory
as in each step it adds the next lowest-weight edge that will not form a cycle to the minimum spanning forest.
Which algorithm is used to find the minimum spanning tree?
Prim’s algorithm
is one way to find a minimum spanning tree (MST). A minimum spanning tree (shown in red) minimizes the edges (weights) of a tree.
How many different minimum spanning trees does it have?
There is only
one
minimum spanning tree in the graph where the weights of vertices are different.
What are the applications of minimum spanning tree Mcq?
| Que. An immediate application of minimum spanning tree ______ | b. handwriting recognition | c. fingerprint detection | d. soft computing | Answer:handwriting recognition |
|---|
What is a minimum spanning tree Mcq?
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges(V – 1 ) of a connected, edge-weighted undirected graph G(V, E) that connects all the vertices together, without any cycles and with the minimum possible total edge weight.
Which of the following graph can definitely not be a spanning tree of some graph?
A
disconnected graph
does not have any spanning tree, as it cannot be spanned to all its vertices. We found three spanning trees off one complete graph. A complete undirected graph can have maximum n
n – 2
number of spanning trees, where n is the number of nodes.
Which of the following is false a the spanning trees do not have any cycles?
Explanation:
every spanning tree has n – 1 edges if the graph has n edges and has no cycles.
What is the weight of the minimum spanning tree using the Kruskal’s algorithm?
What is the weight of the minimum spanning tree using the Kruskal’s algorithm? So, the weight of the MST is
19
.
Which of the following problems is not solved using dynamic programming?
9. Which of the following problems is NOT solved using dynamic programming? Explanation: The
fractional knapsack problem
is solved using a greedy algorithm.
Is Kruskal better than prim?
Prim’s algorithm is significantly faster in the limit when you’ve got a really dense graph with many more edges than vertices.
Kruskal performs better in typical situations (sparse graphs) because it uses simpler data structures
.
How many edges does a minimum spanning tree have?
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.
Which of the following statements is always correct for any two spanning trees for a graph?
Narrowing the scope further: I shall only consider graphs with no loops and with no multiple edges – in what follows a pair of vertices may be connected with at most one edge. Hence, the right answer is option 2 “
Selected vertices have same degree
”
