Tie set and tie-set matrix
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The document defines a tie-set as a set of branches that form a closed path or loop in a graph containing one link and remaining twigs. A tie-set is also known as a fundamental circuit or f-circuit. The number of tie-sets or loops in a graph equals the number of links. A tie-set matrix describes how branches constitute loops in a graph using an ordered list and reference direction for each loop. Examples of tie-set matrices for different trees are provided.
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Tie set and tie-set matrix
- 1. Tie Set and Tie Set Matrix Mrs.V.SrirengaNachiyar, Assistant Professor (Sr. Gr.), Department of Electronics and Communication Engineering, Ramco Institute of Technology, Rajapalayam
- 2. TIE-SET • A tie-set is a set of branches that form a closed path in a graph such that the closed path contains one link and remainders are twigs. • The closed path is also known as loop. • A tree of a graph does not have any closed path. • Upon adding a link to the tree a closed path or loop is created. • Therefore on adding each link creates one loop and • So the number of loops in a graph will be equal to number of links.
- 3. TIE-SET • In other words, the number of tie-sets will be equal to number of links. • For a graph with b branches and n nodes, the possible tie-sets are given by (b − n + 1). • The tie-set is also called as fundamental circuit or f- circuit. • Therefore, a fundamental tie-set is a tie-set formed by one and only one link and a set of twigs.
- 4. TIE-SET
- 5. TIE SET MATRIX • Tie set matrix is used to describe the way in which the branches constitute loops or circuits in a graph. • An arbitrary orientation is specified for each loop using an ordered list of its branches and nodes. • The reference direction of the f-loop is taken as that of the link.
- 10. TIE SET MATRIX Example Tree 1
- 11. TIE SET MATRIX Example Tree 1
- 12. TIE SET MATRIX Example Tree 1
- 13. TIE SET MATRIX Example Tree 1
- 14. TIE SET MATRIX Example Tree 2
- 15. TIE SET MATRIX Example Tree 2
- 16. TIE SET MATRIX Example Tree 2
- 17. TIE SET MATRIX Example Tree 3
- 18. TIE SET MATRIX Example Tree 3
- 19. TIE SET MATRIX Example Tree 3