论文标题
部分可观测时空混沌系统的无模型预测
Grundy domination and zero forcing in regular graphs
论文作者
论文摘要
给定有限图$ g $，序列$（v_1，\ ldots，v_k）$的最大长度在$ g $中的顶点，每个$ v_i $占主导地位的顶点，该顶点不受任何顶点的主导$ \ \ \ {v_1，\ ldots，\ ldots，v_ {i-1-1} $ normination normantination normantion normination normantion normination normistion normination。 gr}(G)$, of $G$. A small modification of the definition yields the Z-Grundy domination number, which is the dual invariant of the well-known zero forcing number.在本文中，我们证明了$γ_{\ rm gr}（g）\ geq \ frac {n + \ lceil \ frac {k} {2} {2} \ rceil-2} {k-1} {k-1} $在每个连接$ k $ k $ n $ n $ n $ n $ n $ k _ bar} $ k _ $ k _4} $ 1} $ 1} $ k + 1}和$ k + 1}和$ k + 1}和$ 1} $ 1} $ {k-1} $ comploss中在这种情况下，$ k = 3 $的绑定减少到$γ_ {\ rm gr}（g）\ geq \ frac {n} {2} $，我们用$γ_{\ rm gr}（g）（g）（g）= \ frac {n} {n} = 2} $。如果$ g $与$ k_4 $和$ k_ {3,3} $不同，则$ \ frac {n} {2} $也是连接的立方图的零强迫数的上限，我们表征了获得此限制的连接的立方图。
Given a finite graph $G$, the maximum length of a sequence $(v_1,\ldots,v_k)$ of vertices in $G$ such that each $v_i$ dominates a vertex that is not dominated by any vertex in $\{v_1,\ldots,v_{i-1}\}$ is called the Grundy domination number, $γ_{\rm gr}(G)$, of $G$. A small modification of the definition yields the Z-Grundy domination number, which is the dual invariant of the well-known zero forcing number. In this paper, we prove that $γ_{\rm gr}(G) \geq \frac{n + \lceil \frac{k}{2} \rceil - 2}{k-1}$ holds for every connected $k$-regular graph of order $n$ different from $K_{k+1}$ and $\bar{2C_4}$. The bound in the case $k=3$ reduces to $γ_{\rm gr}(G) \geq \frac{n}{2}$, and we characterize the connected cubic graphs with $γ_{\rm gr}(G)=\frac{n}{2}$. If $G$ is different from $K_4$ and $K_{3,3}$, then $\frac{n}{2}$ is also an upper bound for the zero forcing number of a connected cubic graph, and we characterize the connected cubic graphs attaining this bound.
