On the Location of Roots of Independence Polynomials |
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| Authors: | JI Brown CA Hickman RJ Nowakowski |
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| Institution: | (1) Department of Mathematics and Statistics and Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5;(2) The Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada, M5T 3J1;(3) Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5 |
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| Abstract: | The independence polynomial of a graph G is the function i(G, x) = 
k 0
i
k
x
k, where i
k is the number of independent sets of vertices in G of cardinality k. We prove that real roots of independence polynomials are dense in (– , 0], while complex roots are dense in  , even when restricting to well covered or comparability graphs. Throughout, we exploit the fact that independence polynomials are essentially closed under graph composition. |
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| Keywords: | graph independence polynomial roots |
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