What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?
Answer: C $1-2-3-4-5-6-7-8-9$ $(2,5,8)$ is the maximal independent set for a chain of $9$ nodes. If we add any other node to the set then it will not be MIS.
1--2--3--4--5--6--7--8--9
MIS of size 5 : 1,3,5,7,9
MIS os size 4 : 2,4,6,8
MIS of size 3 : 2,5,8
MIS is independent set in which If we add any other node (outside MIS) to the set then it will be no more MIS.
so smallest size of MIS is 3 Option C
@AKASH G more can exist
but here example which u have given, can't take that, as we can include here 9 too, so size will become 4 not 3
If you have somemore question related to this or resources please add .
@MANSI_SOMANI got it 👍 thanks!
If we try to add any vertext in set {2,5,8} then that vertex will be adjacent to 2 or 5 or 8 like if we want to add 4 that will be adjacent to 5 so independent set property will be lost.We cant take 2 vertices as Maximal property will not hold, we have to make it mamximum in such a way that the no of vertices will be minimum to make it MIS.1,4,7 is also a MIS
so C) is the ans
A set of vertices is called independent set such that no two vertices in the set are adjacent. A maximal independent set (MIS) is an independent set which is not subset of any other independent set.
The question is about smallest MIS. We can see in below diagram, the three highlighted vertices (2nd, 5th and 8th) form a maximal independent set (not subset of any other MIS) and smallest MIS.
0----0----0----0----0----0----0----0----0
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