A flow graph F with entry node (1) and exit node (11) is shown below:

F1 R.S Madhu 06.06.20 D1

How many nodes are there in the longest independent path?

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UGC NET Computer Science (Paper 2) Dec 2019 Paper
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  1. 6
  2. 7
  3. 8
  4. 9

Answer (Detailed Solution Below)

Option 3 : 8
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Detailed Solution

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Concept

A linearly independent path is any path that introduces at least one new edge that is not included in any other linearly independent path.

Data

From the graph shown above, following are possible independent paths.

Path 1: 1-11

Path 2: 1-2-3-4-5-10-1-11

Path 3: 1-(2,3)-6-8-9-10-1-11

Path 4: 1-(2,3)-6-7-9-10-1-11

Each of the above path introduces a new edge. And Path 3 and Path 4 are longest independent paths with 8 nodes.

Note that, a path like 1-(2,3)-4-5-10-1-2-3-6-8-9-10-1-11 is not an independent path because it includes already specified edges and doesn’t exclusively add new edges.
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