Understanding Trees in Graph Theory
In graph theory, a tree is a special type of graph that has unique characteristics. Trees are widely used in various applications, especially in Electrical Engineering.
Key Characteristics of Trees:
- Acyclic Nature: Trees are defined as acyclic graphs, meaning they do not contain any cycles or closed paths.
- Connected Structure: A tree is connected, meaning there is a path between any two vertices. However, this connectivity does not lead to cycles.
- Vertices and Edges: A tree with 'n' vertices always has 'n-1' edges. This relationship contributes to the absence of cycles.
Closed Paths in Trees:
- Definition of Closed Paths: A closed path (or cycle) in a graph is a path that starts and ends at the same vertex without retracing any edges.
- Implication in Trees: Since trees are acyclic, they inherently have no closed paths. Each of the connections (edges) between vertices allows traversal without revisiting any edge.
Conclusion:
Given the definition and properties of trees, it is clear that:
- The number of closed paths in a tree is zero.
Thus, the correct answer to the question about the number of closed paths in a tree is option C) 0. This fundamental property of trees is crucial in understanding their structure and behavior in various applications, including network design and data organization in Electrical Engineering.