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A tree is a connected graph in which only 1 path exist between any two vertices of the graph i.e. if the graph has no cycles.
A spanning tree of a connected graph G is a tree which includes all the vertices of the graph G.There can be more than one spanning tree for a connected graph G.
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What is spanning tree in data structure?
A spanning tree is a tree associated with a network. All the nodes of the graph appear on the tree once. A minimum spanning tree is a spanning tree organized so that the total edge weight between nodes is minimized.
Can dijkstra's algorithm produce a spanning tree?
yes, but a shortest path tree, not a minimum spanning tree
Applications of minimum cost spanning tree?
Minimum cost spanning tree is used for Network designing.(like telephone, electrical, hydraulic, TV cable, computer, road)
What is krushkal algorithm?
Kruskal's algorithm is an algorithm in graph theory that finds a minimum spanning tree for a connected weighted graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. If the graph is not connected, then it finds a minimum spanning forest (a minimum spanning tree for each connected component). Kruskal's algorithm is an example of a greedy algorithm.
What is the complexity of kruskal's minimum spanning tree algorithm on a graph with n nodes and e edges?
o(eloge)
What is spanning tree in data structure?
A spanning tree is a tree associated with a network. All the nodes of the graph appear on the tree once. A minimum spanning tree is a spanning tree organized so that the total edge weight between nodes is minimized.
Can dijkstra's algorithm produce a spanning tree?
yes, but a shortest path tree, not a minimum spanning tree
What is STP called now?
STP (Spanning Tree Protocol) is still referred to as STP. However, there are newer variations of STP such as Rapid Spanning Tree Protocol (RSTP) and Multiple Spanning Tree Protocol (MSTP).
What is Difference between sink tree and spanning tree?
While the other, more technical answer is correct, a simpler answer would be to just say that with a sink tree, each item or category leads to the next and no attempt is made to connect them to each other. A spanning tree would make those connections between categories and items, and would be far more complex on each level. Envision a large house with many doors. There may be many ways to get to the living room from each part of the house, but the sink tree would list the shortest, and then the shortest to the living room, etc., whereas a spanning tree would list all probable pathways from one category to another,
What effect will the command spanning-tree link-type point-to-point have on a rapid spanning tree port?
The port will rapidly transition to forwarding.
What is a characteristic of Spanning Tree Protocol?
A spanning tree protocol, or STP, is characteristic to a LAN. It provides a loop-free topology for networks within the system.
What is difference between tree and hybrid topology?
no difference,,,tree and hybrid are same.
How can you find minimum spanning trees?
Minimum spanning trees can be found using algorithms like Prim's algorithm or Kruskal's algorithm. These algorithms work by starting with an empty spanning tree and iteratively adding edges with the smallest weights until all vertices are connected. The resulting tree will have the minimum total weight possible.
Applications of minimum cost spanning tree?
Minimum cost spanning tree is used for Network designing.(like telephone, electrical, hydraulic, TV cable, computer, road)
Prove that a graph G is connected if and only if it has a spanning tree?
Proving this is simple. First, you prove that G has a spanning tree, it is connected, which is pretty obvious - a spanning tree itself is already a connected graph on the vertex set V(G), thus G which contains it as a spanning sub graph is obviously also connected. Second, you prove that if G is connected, it has a spanning tree. If G is a tree itself, then it must "contain" a spanning tree. If G is connected and not a tree, then it must have at least one cycle. I don't know if you know this or not, but there is a theorem stating that an edge is a cut-edge if and only if it is on no cycle (a cut-edge is an edge such that if you take it out, the graph becomes disconnected). Thus, you can just keep taking out edges from cycles in G until all that is left are cut-gees. Since you did not take out any cut-edges, the graph is still connected; since all that is left are cut-edges, there are no cycles. A connected graph with no cycles is a tree. Thus, G contains a spanning tree. Therefore, a graph G is connected if and only if it has a spanning tree!
Prove that a graph G is connected and only if it has a spanning tree?
Proving this is simple. First, you prove that G has a spanning tree, it is connected, which is pretty obvious - a spanning tree itself is already a connected graph on the vertex set V(G), thus G which contains it as a spanning sub graph is obviously also connected. Second, you prove that if G is connected, it has a spanning tree. If G is a tree itself, then it must "contain" a spanning tree. If G is connected and not a tree, then it must have at least one cycle. I don't know if you know this or not, but there is a theorem stating that an edge is a cut-edge if and only if it is on no cycle (a cut-edge is an edge such that if you take it out, the graph becomes disconnected). Thus, you can just keep taking out edges from cycles in G until all that is left are cut-gees. Since you did not take out any cut-edges, the graph is still connected; since all that is left are cut-edges, there are no cycles. A connected graph with no cycles is a tree. Thus, G contains a spanning tree. Therefore, a graph G is connected if and only if it has a spanning tree!
What is the difference between tree and forest?
A tree is one tree and a forest is many trees.
