论文标题
在距离均衡的广义彼得森图上
On distance-balanced generalized Petersen graphs
论文作者
论文摘要
连接的图形$ g $直径$ {\ rm diam}（g）\ ge \ ell $是$ \ ell $ -distance-balanced如果$ | w_ | w_ {xy} | = | w_ {yx {yx} | $ for每个$ x，y \ in v（g）in v in $ d_ { $ g $的顶点接近$ x $，而不是$ y $。我们证明，普遍的彼得森图$ gp（n，k）$是$ {\ rm diam}（gp（n，k））$ - 距离均值，前提是$ n $相对于$ k $足够大。这部分解决了Miklavič和šparl\ cite {Miklavic：2018}提出的猜想。当$ n $相对于$ k $，我们还确定$ {\ rm diam}（gp（n，k））$。
A connected graph $G$ of diameter ${\rm diam}(G) \ge \ell$ is $\ell$-distance-balanced if $|W_{xy}|=|W_{yx}|$ for every $x,y\in V(G)$ with $d_{G}(x,y)=\ell$, where $W_{xy}$ is the set of vertices of $G$ that are closer to $x$ than to $y$. We prove that the generalized Petersen graph $GP(n,k)$ is ${\rm diam}(GP(n,k))$-distance-balanced provided that $n$ is large enough relative to $k$. This partially solves a conjecture posed by Miklavič and Šparl \cite{Miklavic:2018}. We also determine ${\rm diam}(GP(n,k))$ when $n$ is large enough relative to $k$.
