Tie set and tie-set matrix

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 .

6. TIE SET MATRIX

7. TIE SET MATRIX

8. TIE SET MATRIX

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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