A note on purely imaginary independence roots. (English) Zbl 1448.05111
Summary: The independence polynomial of a graph is the generating polynomial for the number of independent sets of each cardinality and its roots are called independence roots. We investigate here purely imaginary independence roots. We show that for all \(k\geq 4\), there are connected graphs with independence number \(k\) and purely imaginary independence roots. We also show that every graph is an induced subgraph of a connected graph with purely imaginary independence roots and classify every purely imaginary number of the form \(ri,r\) rational, that is an independence root.
MSC:
| 05C31 | Graph polynomials |
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
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