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
Question
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
Solution
The false statement is c. Removing one edge from Spanning tree will not make the graph disconnected.
Here's why:
a. None of Them - This is not a statement, it's an option. b. The spanning trees do not have cycles - This is true. By definition, a spanning tree is a subgraph that includes all the vertices of the original graph and is also a tree. Therefore, it cannot have cycles. c. Removing one edge from Spanning tree will not make the graph disconnected - This is false. In a spanning tree, removing any edge will disconnect the graph because a tree is minimally connected, which means there's exactly one path between any two vertices. Removing any edge will break this path, disconnecting the graph. d. Minimum Spanning Tree have n-1 edges if the Graph has n edges - This is true. A minimum spanning tree is a spanning tree with weight less than or equal to the weight of every other spanning tree. The number of edges in a tree with n vertices is always n-1, regardless of whether it's a minimum spanning tree or not.
Similar Questions
Every graph has only one minimum spanning tree. State true or false.a)Falseb)True
Which of the following statements about spanning trees is false?AA spanning tree of a graph G is a subgraph that includes all vertices of GBA spanning tree can be a disconnected graphCA spanning tree has n−1 edges where n is the number of vertices in the original graphDEvery connected graph has at least one spanning tree.
Which of the following statements about trees in graph theory is true?AA tree can contain cyclesBA tree is always a disconnected graphCA tree with n vertices has n−1 edgesDA tree has at least one cycle
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
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
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.