论文标题
具有相同统治和独立数量的图形
Graphs with equal Grundy domination and independence number
论文作者
论文摘要
Grundy的支配数字，$ {γ_{\ rm gr}}（g）$，$ g $的最大长度是序列$的最大长度（v_1，v_2，v_2，\ ldots，v_k）$ g $中的顶点$不属于任何关闭的邻里$ n [v_j] $的顶点，其中$ j <i $。众所周知，任何图$ g $的Grundy统治数大于或等于上部支配数字$γ（g）$，这又大于或等于独立性数字$α（g）$。在本文中，我们使用$γ（g）= {γ_ {\ rm gr}}}（g）$及其由$α（g）= {γ_ {γ_ {\ rm gr}}（g）$组成的$ g $的研究$ g $的研究。我们表征了所有无孪晶连接图之间的后一类图形，提供了这些图形的许多属性，并证明了Hyperuibes是此类的成员。此外，我们为图$ g $提供了几个必要的条件，其中$γ（g）= {γ_ {\ rm gr}}}}（g）$，并呈现此类图的大家庭。
The Grundy domination number, ${γ_{\rm gr}}(G)$, of a graph $G$ is the maximum length of a sequence $(v_1,v_2,\ldots, v_k)$ of vertices in $G$ such that for every $i\in \{2,\ldots, k\}$, the closed neighborhood $N[v_i]$ contains a vertex that does not belong to any closed neighborhood $N[v_j]$, where $j<i$. It is well known that the Grundy domination number of any graph $G$ is greater than or equal to the upper domination number $Γ(G)$, which is in turn greater than or equal to the independence number $α(G)$. In this paper, we initiate the study of the class of graphs $G$ with $Γ(G)={γ_{\rm gr}}(G)$ and its subclass consisting of graphs $G$ with $α(G)={γ_{\rm gr}}(G)$. We characterize the latter class of graphs among all twin-free connected graphs, provide a number of properties of these graphs, and prove that the hypercubes are members of this class. In addition, we give several necessary conditions for graphs $G$ with $Γ(G)={γ_{\rm gr}}(G)$ and present large families of such graphs.
