Consider a undirected graph G with vertices { A, B, C, D, E}. In graph G, every edge has distinct weight. Edge CD is edge with minimum weight and edge AB is edge with maximum weight. Then, which of the following is false?ans.Every minimum spanning tree of G must contain CDG has a unique minimum spanning treeIf AB is in a minimum spanning tree, then its removal must disconnect GNo minimum spanning tree contains AB Previous Marked for Review Next
Question
Consider a undirected graph G with vertices { A, B, C, D, E}. In graph G, every edge has distinct weight. Edge CD is edge with minimum weight and edge AB is edge with maximum weight. Then, which of the following is false?ans.Every minimum spanning tree of G must contain CDG has a unique minimum spanning treeIf AB is in a minimum spanning tree, then its removal must disconnect GNo minimum spanning tree contains AB Previous Marked for Review Next
Solution
The statement "G has a unique minimum spanning tree" is false.
In a graph, a minimum spanning tree (MST) is a subset of the edges of the graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. However, it's possible for a graph to have more than one minimum spanning tree, if there are multiple ways to connect all the vertices together with the same total weight.
In this case, the graph G could potentially have multiple minimum spanning trees. The fact that every edge has a distinct weight does not necessarily mean that there is a unique minimum spanning tree. For example, consider a graph with vertices {A, B, C, D, E} and edges with weights {1, 2, 3, 4, 5}. The edge with minimum weight is CD (1), and the edge with maximum weight is AB (5). A minimum spanning tree could be {CD, BC, BE, EA}, with a total weight of 10. But another minimum spanning tree could be {CD, BD, DE, EA}, also with a total weight of 10. So, the statement "G has a unique minimum spanning tree" is false.
Similar Questions
Let G be an undirected connected graph with distinct edge weight. Let emax be the edge with maximum weight and emin the edge with minimum weight. Which of the following statements is false?Marks : 1Negative Marks : 0Answer hereEvery minimum spanning tree of G must contain eminG has a unique minimum-spanning treeNo minimum spanning tree contains emaxIf emax is in a minimum spanning tree, then its removal must disconnect GClearPrevNext
Consider a undirected graph G with vertices { A, B, C, D, E}. In graph G, every edge has distinct weight. Edge CD is edge with minimum weight and edge AB is edge with maximum weight. Then, which of the following is false?
Every graph has only one minimum spanning tree. State true or false.a)Falseb)True
I. 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.I is true and II is falseI is false and II is trueBoth I and II are falseBoth I and II are true Previous Marked for Review Next
Which of the following is falsea. None of Themb. The spanning trees do not have cyclesc. Removing one edge from Spanning tree will not make the graph disconnected. d. Minimum Spanning Tree have n-1 edges if the Graph has n edges
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