Domination polynomials of even-order friendship graphs have three real roots with monotonic limits to -1 ± 1/√2 and magnitude bound |z| ≤ 1 + √(n/log 2); book graphs have complete root limit sets with parity-dependent real roots; both families lack nonzero integer roots.
Alikhani, On the domination polynomial of some graph operations,Int
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On roots of domination polynomials for friendship and book graphs
Domination polynomials of even-order friendship graphs have three real roots with monotonic limits to -1 ± 1/√2 and magnitude bound |z| ≤ 1 + √(n/log 2); book graphs have complete root limit sets with parity-dependent real roots; both families lack nonzero integer roots.