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A tree is
connected sub-graph of a network which consists of all the nodes of original graph but no closed path
connected graph of a network with no closed path
connected sub-graph of a network which consists of all the nodes of original graph with closed path
All of them
connected sub-graph of a network which consists of all the nodes of original graph but no closed path
A tree in graph theory applied to electrical networks is a subgraph that includes all nodes (vertices) of the original graph while maintaining a connected structure without any closed loops. It effectively represents the minimum number of branches required to connect all nodes in a network, with a total of nтИТ1 branches for n nodes.
A tree in graph theory applied to electrical networks is a subgraph that includes all nodes (vertices) of the original graph while maintaining a connected structure without any closed loops. It effectively represents the minimum number of branches required to connect all nodes in a network, with a total of nтИТ1 branches for n nodes.
btтАЛ=nтИТ1 тАФ where btтАЛ is the number of branches in the tree and n is the number of nodes.
l=bтИТn+1 тАФ where l is the number of links (co-tree branches) in the graph.
The principle relies on the relationship between nodes and branches in a network graph. To ensure all nodes are connected without forming a closed path (which would create redundancy or loops), the number of branches btтАЛ must satisfy the condition btтАЛ=nтИТ1. Any addition of a branch to a tree creates a fundamental loop, while the removal of any branch from a tree results in a disconnected graph.
A tree must contain all n nodes of the original graph.
A tree contains exactly nтИТ1 branches.
A tree cannot contain any closed paths (loops).
Adding any branch to a tree creates exactly one closed loop.
Simplifies complex network analysis by reducing redundant paths.
Forms the basis for determining cut-sets and loop equations (KCL and KVL).
Does not represent all possible paths for current flow.
Requires additional links to fully describe a complete planar or non-planar network.
Determining independent loop equations in network analysis.
System reliability and topological connectivity studies.
A co-tree is the complement of a tree, consisting of all branches not included in the tree.
Option B is incorrect because a connected graph with no closed path is a definition of a tree, but it lacks the requirement of including ALL nodes of the original graph.
Option C is incorrect because a tree, by definition, must have no closed paths.
A is correct тАФ A tree is a connected subgraph that spans every node of the original graph while maintaining an acyclic (loop-free) structure.
Always remember that in network topology, for a graph with n nodes and b branches, the tree always has nтИТ1 branches, regardless of how many loops exist in the original network.