This study examines the domination polynomials of friendship graphs and book graphs, focusing on unanswered questions related to these families [Alikhani, Brown and Jahari, on the domination polynomials of friendship graphs, Filomat \textbf{30}(1) (2016) 169--178]. For the friendship graph $F_n$, with even $n$, we show that the polynomial $D(F_n,x)$ has exactly three real zeros: $0$ and two simple zeros in the intervals $(-2,-1)$ and $(-1,0)$. We further show that these two nonzero zeros have monotonic variation and converge to $-1-\frac{1}{\sqrt2}$ and $-1+\frac{1}{\sqrt2}$, respectively. We obtain the quantitative approximation $(|z|-1)^2\log |z|\le n$ for any complex zeros of $D(F_n,x)$, resulting in the explicit bound $|z|\le 1+\sqrt{\tfrac{n}{\log 2}}$. For book graphs $B_n$, we ascertain the comprehensive limit set of domination roots and establish results about the presence of real roots contingent on parity. We provide a partial answer to the integer-root an issue by establishing that friendship and book graphs have no nonzero integer domination roots, whereas for corona families, the only nonzero integer root is $-2$.

翻译：本研究考察了友谊图与书图的支配多项式，重点关注与这些图族相关的未解问题 [Alikhani, Brown and Jahari, on the domination polynomials of friendship graphs, Filomat \textbf{30}(1) (2016) 169--178]。对于友谊图 $F_n$（$n$ 为偶数），我们证明多项式 $D(F_n,x)$ 恰好有三个实根：$0$ 以及位于区间 $(-2,-1)$ 和 $(-1,0)$ 内的两个单根。进一步表明，这两个非零根具有单调变化性，并分别收敛于 $-1-\frac{1}{\sqrt2}$ 和 $-1+\frac{1}{\sqrt2}$。对于 $D(F_n,x)$ 的任何复根，我们得到了定量近似关系 $(|z|-1)^2\log |z|\le n$，进而导出显式上界 $|z|\le 1+\sqrt{\tfrac{n}{\log 2}}$。针对书图 $B_n$，我们确定了支配根的完整极限集，并根据奇偶性建立了实根存在性的结论。关于整数根问题，我们给出了部分解答：友谊图与书图不存在非零整数支配根，而对于冠图族，唯一的非零整数根为 $-2$。