IndependencePolynomial returns the independence polynomial for the graph G in the variable x.
For the following example, its calculation took over 20 minutes and still hasn't produced a result, and what's fatal is that it has consumed 4G memory.
IndependencePolynomial(G1, x) # be careful
I use codes in the link https://github.com/pernici/hobj.
It produced results quickly (It takes approximately 5 seconds.). So I think the built-in function " IndependencePolynomial " should be able to be improved. (Of course we are usually very concerned about their coefficients)
Their coefficients of the independent polynomial of G1 are as follows.
[340649, 12329124, 68797662, 140606548, 139481127, 77027880, 25546428, 5303544, 700911, 58580, 2982, 84, 1]
It tells me the total number of independence sets with size 12 is 340649.