Question

# a graph G that is a line on n vertices. (That is, the vertices are labelled 1 to n, and there is an edge from 1 to

2, 2 to 3, etc.)

if we have a simple graph like the one described, how could i find and prove the number of INDEPENDENT sets contained in graph G (I.E. so there is not an edge connecting the two vertices) for each set (I.E. INDEPENDENT)? I want to find a general answer in terms of n (i.e "For n vertices the number of independent sets is the nth prime.")

Thank you!

I have found the forumula 3^{n/3 }to calculate the max number of independent sets on a graph, but I'm not sure how or why this is true.

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