What is the purpose of MST in graph theory?AConnect all vertices with minimum weight of edgesBConnect all the nodes in various waysCConnect all nodes without regard to costBerikutnya
Question
What is the purpose of MST in graph theory?AConnect all vertices with minimum weight of edgesBConnect all the nodes in various waysCConnect all nodes without regard to costBerikutnya
Solution
The purpose of the Minimum Spanning Tree (MST) in graph theory is to connect all vertices with the minimum weight of edges.
Here's a step-by-step explanation:
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Graph Theory: This is a branch of mathematics that studies the relationship between pairs of objects and the properties of those relationships. In graph theory, objects are represented as vertices (or nodes), and the relationships between them are represented as edges.
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Spanning Tree: A spanning tree of a graph is a tree that includes every vertex of the graph. It is a subgraph that includes all the vertices of the original graph.
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Minimum Spanning Tree (MST): The MST is a special type of spanning tree. The goal of the MST is to minimize the total weight of the edges in the tree. In other words, if you add up the weights of all the edges in the tree, the total should be as small as possible.
So, the purpose of the MST in graph theory is to find the most efficient way to connect all the vertices in a graph. This has many practical applications, such as in network design, where you might want to connect all the computers in a network using as little cable as possible.
Similar Questions
What is a minimum spanning tree (MST) in graph theory?Select one:a. A subtree of a graph that connects all the vertices with the minimum possible total edge weight.b. Any subtree of a graph that includes all of its vertices.c. A subtree that includes the shortest path between every pair of vertices.d. A tree with the minimum number of edges possible.
Consider the graph shown above. Which of the following are the edges in the MST of the given graph?ans.(a-d)(d-c)(d-b)(d-e)(c-a)(a-d)(d-c)(d-b)(d-e)(a-c)(c-d)(d-b)(d-b)(c-a)(a-d)(d-b)(d-e) Previous Marked for Review Next
If all the weights of the graph are positive, then the minimum spanning tree of the graph is a minimum cost subgraphII. A subgraph is a graph formed from a subset of the vertices and edges of the original graph. And the subset of vertices includes all endpoints of the subset of the edges.
Which is true statement in the followinga.Both of aboveb.Kruskal’s algorithm (choose best non-cycle edge) is better than prim’s(choose best tree edge) when the graph has relatively few edges.c.Kruskal’s algorithm is used to find MST of a graph , time complexity of this algorithm is O(EV)d.Kruskal’s algorithm is multiple source technique for finding MST.
. If all the weights of the graph are positive, then the minimum spanning tree of the graph is a minimum cost subgraphII. A subgraph is a graph formed from a subset of the vertices and edges of the original graph. And the subset of vertices includes all endpoints of the subset of the edges. ans.Both I and II are falseBoth I and II are trueI is true and II is falseI is false and II is true Previous Marked for Review Next
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