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Consider the following given figure in which the graph and tree (dotted) are shown: Choose the fundamental loops which include the set of lines.

Consider the following given figure in which the graph and tree (dotted) are shown: Choose the fundamental loops which include the set of lines. Correct Answer (1, 5, 3), (5, 4, 2) and (3, 4, 6)

Twig: The branch of a tree is specifically known as “Twig”, indicated by a thick line segment.

Any tree with ‘n’ nodes has n – 1 twig.

Co tree: The set of branches other than tree branches collectively form a co tree.

Link/chord: The branches of a co tree specifically called as links indicated by dotted.

Any particular co tree of a graph has b – n + 1 links.

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[ alt="F2 Shubham 4.9.20 Pallavi D 12" src="//storage.googleapis.com/tb-img/production/20/09/F2_Shubham_4.9.20_Pallavi_D%2012.png" style="width: 175px; height: 121px;">

[ alt="F2 Shubham 4.9.20 Pallavi D 13" src="//storage.googleapis.com/tb-img/production/20/09/F2_Shubham_4.9.20_Pallavi_D%2013.png" style="width: 204px; height: 119px;">

Fundamental loop

  • The fundamental loop is a closed path of a graph that is formed by only one link and remaining as twigs.
  • The number of fundamental loops for any given graph is equal to the number of links. Links = ( b – n + 1)
  • Those fundamental loops are also called as “Fundamental circuits”
  • The fundamental loop currents are called as “Tie set current” and their orientation is given by link in it.

 

Example:

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[ alt="F2 Shubham 4.9.20 Pallavi D 15" src="//storage.googleapis.com/tb-img/production/20/09/F2_Shubham_4.9.20_Pallavi_D%2015.png" style="width: 128px; height: 172px;">

fl1 → abe → i1

fl2 → cdb → i2

fl3 → fde → i3

Calculation:

Method 1

Total nodes are 4 and branches are 6

Fundamental loops = links

= 6 – 4 + 1

= 3

Only option 1 satisfies this.

Method 2

 From the given graph tree is given by dotted lines

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[ alt="F2 Shubham 4.9.20 Pallavi D 17" src="//storage.googleapis.com/tb-img/production/20/09/F2_Shubham_4.9.20_Pallavi_D%2017.png" style="width: 142px; height: 216px;">

fl1 → 153 → i1

fl2 → 542 → i2

fl3 → 346 → i3

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