论文标题
计算最小的双重解析集和图层太阳图的强度度和强度度
Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of Layer Sun Graph
论文作者
论文摘要
令$ g $为有限的，连接的订单图，至少为2，而顶点套装$ v（g）$和edge set $ e（g）$。图$ g $的一套$ s $顶点是$ g $的双重解析，如果每两个不同的$ g $的顶点被约两个顶点的$ s $偶尔解决。图形$ g $的最低偶尔解析集合是具有最低基数的双重解析集，并用$ψ（g）$表示。在本文中，首先，我们构建了一类订单$ 2N+σ_{r = 1}^{k-2}^{k-2} nm^{r} $，由$ lsg（n，m，k）$表示，并将这些图称为带有参数$ n $ n $，$ m $和$ k $的图层太阳图。此外，我们计算了最小的双重分辨集和Layer Sun Graph $ LSG（N，M，K）$的强度度量尺寸以及Layer Sun Graph $ LSG（N，M，K）$的线图。
Let $G$ be a finite, connected graph of order of at least 2, with vertex set $V(G)$ and edge set $E (G)$. A set $S$ of vertices of the graph $G$ is a doubly resolving set for $G$ if every two distinct vertices of $G$ are doubly resolved by some two vertices of $S$. The minimal doubly resolving set of vertices of graph $G$ is a doubly resolving set with minimum cardinality and is denoted by $ψ(G)$. In this paper, first, we construct a class of graphs of order $2n+ Σ_{r=1}^{k-2}nm^{r}$, denoted by $LSG(n,m, k)$, and call these graphs as the layer Sun graphs with parameters $n$, $m$ and $k$. Moreover, we compute minimal doubly resolving sets and the strong metric dimension of layer Sun graph $LSG(n,m, k)$ and the line graph of the layer Sun graph $LSG(n,m, k)$.
