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- W2964092672 abstract "The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size and its roots are called independence roots. We investigate the stability of such polynomials, that is, conditions under which the independence roots lie in the left half-plane. We use results from complex analysis to determine graph operations that result in a stable or nonstable independence polynomial. In particular, we prove that every graph is an induced subgraph of a graph with stable independence polynomial. We also show that the independence polynomials of graphs with independence number at most three are necessarily stable, but for larger independence number, we show that the independence polynomials can have roots arbitrarily far to the right." @default.
- W2964092672 created "2019-07-30" @default.
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- W2964092672 date "2018-03-02" @default.
- W2964092672 modified "2023-09-24" @default.
- W2964092672 title "On the Stability of Independence Polynomials" @default.
- W2964092672 doi "https://doi.org/10.37236/7280" @default.
- W2964092672 hasPublicationYear "2018" @default.
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